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Markström, Klas

Open this publication in new window or tab >>Latin cubes with forbidden entries### Casselgren, Carl Johan

### Markström, Klas

### Pham, Lan Anh

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 26, no 1, article id P1.2Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Newark: Department of Mathematical Science, University of Delaware, 2019
##### National Category

Discrete Mathematics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-147511 (URN)000456790800002 ()
#####

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##### Funder

Swedish Research Council, 2014-4897
##### Note

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

We consider the problem of constructing Latin cubes subject to the condition that some symbols may not appear in certain cells. We prove that there is a constant y>0 such that if n=2^{k} and A is a 3-dimensional n×n×n array where every cell contains at most γn symbols, and every symbol occurs at most γn times in every line of A, then A is avoidable; that is, there is a Latin cube L of order n such that for every 1 ≤ i,j,k ≤ n, the symbol in position (i,j,k) of L does not appear in the corresponding cell of A.

Originally included in thesis in manuscript form.

Available from: 2018-05-04 Created: 2018-05-04 Last updated: 2019-04-24Bibliographically approvedOpen this publication in new window or tab >>Revisiting the cavity-method threshold for random 3-SAT### Lundow, Per-Håkan

### Markström, Klas

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 99, no 2, article id 022106Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

American Physical Society, 2019
##### National Category

Probability Theory and Statistics
##### Identifiers

urn:nbn:se:umu:diva-162509 (URN)10.1103/PhysRevE.99.022106 (DOI)000458140700001 ()30934345 (PubMedID)
#####

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Available from: 2019-08-21 Created: 2019-08-21 Last updated: 2019-08-21Bibliographically approved

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

A detailed Monte Carlo study of the satisfiability threshold for random 3-SAT has been undertaken. In combination with a monotonicity assumption we find that the threshold for random 3-SAT satisfies α_{3}≤4.262. If the assumption is correct, this means that the actual threshold value for *k*=3 is lower than that given by the cavity method. In contrast the latter has recently been shown to give the correct value for large *k*. Our result thus indicate that there are distinct behaviors for *k* above and below some critical *k _{c}*, and the cavity method may provide a correct mean-field picture for the range above

Open this publication in new window or tab >>Triples of Orthogonal Latin and Youden Rectangles of small order### Jäger, Gerold

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Markström, Klas

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Öhman, Lars-Daniel

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Shcherbak, Denys

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Journal of combinatorial designs (Print), ISSN 1063-8539, E-ISSN 1520-6610, Vol. 27, no 4, p. 229-250Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Discrete Mathematics
##### Identifiers

urn:nbn:se:umu:diva-158857 (URN)10.1002/jcd.21642 (DOI)000459040800001 ()2-s2.0-85059030594 (PubMedID)
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Available from: 2019-05-13 Created: 2019-05-13 Last updated: 2019-05-23Bibliographically approved

We have performed a complete enumeration of non-isotopic triples of mutually orthogonal k × n Latin rectangles for k ≤ n ≤ 7. Here we will present a census of such triples, classified by various properties, including the order of the autotopism group of the triple. As part of this we have also achieved the first enumeration of pairwise orthogonal triples of Youden rectangles. We have also studied orthogonal triples of k×8 rectangles which are formed by extending mutually orthogonal triples with non-trivial autotopisms one row at a time, and requiring that the autotopism group is non-trivial in each step. This class includes a triple coming from the projective plane of order 8. Here we find a remarkably symmetrical pair of triples of 4 × 8 rectangles, formed by juxtaposing two selected copies of complete sets of MOLS of order 4.

Open this publication in new window or tab >>Full subgraphs### Falgas-Ravry, Victor

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Markström, Klas

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Verstraëte, Jacques

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Journal of Graph Theory, ISSN 0364-9024, E-ISSN 1097-0118, Vol. 88, no 3, p. 411-427Article in journal (Refereed) Published
##### Keywords

extremal graph theory, graph discrepancy, graph partitions
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-144161 (URN)10.1002/jgt.22221 (DOI)000432013200004 ()2-s2.0-85034034448 (Scopus ID)
#####

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##### Funder

Swedish Research Council
Available from: 2018-01-23 Created: 2018-01-23 Last updated: 2018-06-13Bibliographically approved

University of California-San Diego.

Open this publication in new window or tab >>On 1-sum flows in undirected graphs### Akbari, Saieed

### Friedland, Shmuel

### Markström, Klas

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Zare, Sanaz

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2016 (English)In: The Electronic Journal of Linear Algebra, ISSN 1537-9582, E-ISSN 1081-3810, Vol. 31, p. 646-665Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

INT LINEAR ALGEBRA SOC, 2016
##### Keywords

L-Flow, gamma-L-Flow, c-Sum flow, Bipartite graph
##### National Category

Discrete Mathematics
##### Identifiers

urn:nbn:se:umu:diva-134293 (URN)10.13001/1081-3810.3003 (DOI)000396550500002 ()
#####

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Available from: 2017-05-09 Created: 2017-05-09 Last updated: 2018-06-09Bibliographically approved

Let G = (V, E) be a simple undirected graph. For a given set L subset of R, a function omega: E -> L is called an L-flow. Given a vector gamma is an element of R-V , omega is a gamma-L-flow if for each v is an element of V, the sum of the values on the edges incident to v is gamma(v). If gamma(v) = c, for all v is an element of V, then the gamma-L-flow is called a c-sum L-flow. In this paper, the existence of gamma-L-flows for various choices of sets L of real numbers is studied, with an emphasis on 1-sum flows. Let L be a subset of real numbers containing 0 and denote L* := L \ {0}. Answering a question from [S. Akbari, M. Kano, and S. Zare. A generalization of 0-sum flows in graphs. Linear Algebra Appl., 438:3629-3634, 2013.], the bipartite graphs which admit a 1-sum R* -flow or a 1-sum Z* -flow are characterized. It is also shown that every k-regular graph, with k either odd or congruent to 2 modulo 4, admits a 1-sum {-1, 0, 1}-flow.

Open this publication in new window or tab >>Random subcube intersection graphs I: cliques and covering### Falgas-Ravry, Victor

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Markström, Klas

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2016 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 23, no 3, article id P3.43Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Random graphs, Random intersection graphs
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-127244 (URN)000385228700002 ()
#####

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Available from: 2016-11-14 Created: 2016-11-03 Last updated: 2018-06-09Bibliographically approved

We study random subcube intersection graphs, that is, graphs obtained by selecting a random collection of subcubes of a fixed hypercube Q_{d} to serve as the vertices of the graph, and setting an edge between a pair of subcubes if their intersection is non-empty. Our motivation for considering such graphs is to model 'random compatibility' between vertices in a large network. For both of the models considered in this paper, we determine the thresholds for covering the underlying hypercube Q_{d} and for the appearance of s-cliques. In addition we pose a number of open problems.

Open this publication in new window or tab >>The scaling window of the 5D Ising model with free boundary conditions### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Markström, Klas

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2016 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 911, p. 163-172Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2016
##### National Category

Atom and Molecular Physics and Optics Probability Theory and Statistics
##### Identifiers

urn:nbn:se:umu:diva-127239 (URN)10.1016/j.nuclphysb.2016.08.003 (DOI)000384565800007 ()
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Available from: 2016-11-14 Created: 2016-11-03 Last updated: 2018-06-09Bibliographically approved

The five-dimensional Ising model with free boundary conditions has recently received a renewed interest in a debate concerning the finite-size scaling of the susceptibility near the critical temperature. We provide evidence in favour of the conventional scaling picture, where the susceptibility scales as L-2 inside a critical scaling window of width 1/L-2. Our results are based on Monte Carlo data gathered on system sizes up to L = 79(ca. three billion spins) for a wide range of temperatures near the critical point. We analyse the magnetisation distribution, the susceptibility and also the scaling and distribution of the size of the Fortuin-Kasteleyn cluster containing the origin. The probability of this cluster reaching the boundary determines the correlation length, and its behaviour agrees with the mean field critical exponent delta = 3, that the scaling window has width 1/L-2.

Open this publication in new window or tab >>Complete graph asymptotics for the Ising and random-cluster models on five-dimensional grids with a cyclic boundary### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Markström, Klas

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 91, article id 022112Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

American Physical Society, 2015
##### National Category

Condensed Matter Physics
##### Identifiers

urn:nbn:se:umu:diva-99987 (URN)10.1103/PhysRevE.91.022112 (DOI)000349910000001 ()
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Available from: 2015-02-17 Created: 2015-02-17 Last updated: 2018-06-07Bibliographically approved

The finite-size scaling behavior for the Ising model in five dimensions, with either free or cyclic boundary, has been the subject of a long-running debate. The older papers have been based on ideas from, e.g., field theory or renormalization. In this paper we propose a detailed and exact scaling picture for critical region of the model with cyclic boundary. Unlike the previous papers our approach is based on a comparison with the existing exact and rigorous results for the FK-random-cluster model on a complete graph. Based on those results we predict several distinct scaling regions in an L -dependent window around the critical point. We test these predictions by comparing with data from Monte Carlo simulations and find a good agreement. The main feature which differs between the complete graph and the five-dimensional model with free boundary is the existence of a bimodal energy distribution near the critical point in the latter. This feature was found by the same authors in an earlier paper in the form of a quasi-first-order phase transition for the same Ising model.

Open this publication in new window or tab >>F-Factors in Hypergraphs Via Absorption### Lo, Allan

### Markström, Klas

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Graphs and Combinatorics, ISSN 0911-0119, E-ISSN 1435-5914, Vol. 31, no 3, p. 679-712Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Hypergraph, k-Graph, F-factor, Minimum degree, Primary 05C65, 05C70, 05C07
##### National Category

Discrete Mathematics
##### Identifiers

urn:nbn:se:umu:diva-92703 (URN)10.1007/s00373-014-1410-8 (DOI)000353232900015 ()2-s2.0-84896417194 (Scopus ID)
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_j_idt371",{id:"formSmash:j_idt184:8:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_j_idt371",multiple:true});
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Available from: 2014-09-01 Created: 2014-09-01 Last updated: 2018-06-07Bibliographically approved

Given integers n ≥ k > l ≥ 1 and a k-graph F with |V(F)| divisible by n, define t k l (n, F) to be the smallest integer d such that every k-graph H of order n with minimum l-degree δl(H) ≥ d contains an F-factor. A classical theorem of Hajnal and Szemerédi in (Proof of a Conjecture of P. Erd˝os, pp. 601–623, 1969) implies that t2 1 (n, Kt) = (1 − 1/t)n for integers t. For k ≥ 3, t k k−1(n, Kk k ) (the δk−1(H) threshold for perfect matchings) has been determined by Kühn and Osthus in (J Graph Theory 51(4):269–280, 2006) (asymptotically) and Rödl et al. in (J Combin Theory Ser A 116(3):613–636, 2009) (exactly) for large n. In this paper, we generalise the absorption technique of Rödl et al. in (J Combin Theory Ser A 116(3):613–636, 2009) to F-factors. We determine the asymptotic values of t k 1 (n, Kk k (m)) for k = 3, 4 and m ≥ 1. In addition, we show that for t > k = 3 and γ > 0, t3 2 (n, K3 t ) ≤ (1− 2 t2−3t+4 +γ )n provided n is large and t|n. We also bound t 3 2 (n, K3 t )from below. In particular, we deduce that t 3 2 (n, K3 4 ) = (3/4+o(1))n answering a question of Pikhurko in (Graphs Combin 24(4):391–404, 2008). In addition, we prove that t k k−1(n, Kk t ) ≤ (1 − t−1 k−1 −1 + γ )n for γ > 0, k ≥ 6 and t ≥ (3 + √ 5)k/2 provided n is large and t|n.

Open this publication in new window or tab >>The discontinuity of the specific heat for the 5D Ising model### Lundow, Per-Håkan

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.### Markström, Klas

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 895, p. 305-318Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-106125 (URN)10.1016/j.nuclphysb.2015.04.013 (DOI)000355032900013 ()
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Available from: 2015-07-14 Created: 2015-07-09 Last updated: 2018-06-07Bibliographically approved

In this paper we investigate the behaviour of the specific heat around the critical point of the Ising model in dimension 5 to 7. We find a specific heat discontinuity, like that for the mean field Ising model, and provide estimates for the left and right hand limits of the specific heat at the critical point. We also estimate the singular exponents, describing how the specific heat approaches those limits. Additionally, we make a smaller scale investigation Of the same properties in dimension 6 and 7, and provide strongly improved estimates for the critical temperature K-c in d = 5, 6, 7 which bring the best MC-estimate closer to those obtained by long high temperature series expansions.