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Sharifzadeh, Maryam

Open this publication in new window or tab >>Limits of latin squares### Garbe, Frederik

### Hancock, Robert

### Hladký, Jan

### Sharifzadeh, Maryam

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_some",{id:"formSmash:j_idt204:0:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_0_j_idt208_otherAuthors",{id:"formSmash:j_idt204:0:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_0_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Discrete Analysis, E-ISSN 2397-3129, Vol. 2023, article id 8Article in journal (Refereed) Published
##### Abstract [en]

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

Alliance of Diamond Open Access Journals, 2023
##### National Category

Discrete Mathematics
##### Identifiers

urn:nbn:se:umu:diva-217362 (URN)10.19086/da.83253 (DOI)001038207600001 ()2-s2.0-85171631393 (Scopus ID)
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##### Funder

EU, Horizon 2020, 648509EU, Horizon 2020, 752426
##### Note

Institute of Mathematics, Czech Academy of Sciences, Czech Republic.

Institut für Informatik, Heidelberg University, Heidelberg, Germany.

Institute of Mathematics, Czech Academy of Sciences, Czech Republic.

University of Warwick, Coventry, UK.

We develop a limit theory of Latin squares, paralleling the recent limit theories ofdense graphs and permutations. We introduce a notion of density, an appropriate version ofthe cut distance, and a space of limit objects — so-called Latinons. Key results of our theoryare the compactness of the limit space and the equivalence of the topologies induced by thecut distance and the left-convergence. Last, using Keevash’s recent results on combinatorialdesigns, we prove that each Latinon can be approximated by a finite Latin square.

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Available from: 2023-11-30 Created: 2023-11-30 Last updated: 2024-01-08Bibliographically approvedOpen this publication in new window or tab >>Stability from graph symmetrisation arguments with applications to inducibility### Liu, Hong

### Pikhurko, Oleg

### Sharifzadeh, Maryam

### Staden, Katherine

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_some",{id:"formSmash:j_idt204:1:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_1_j_idt208_otherAuthors",{id:"formSmash:j_idt204:1:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_1_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. 108, no 3, p. 1121-1162Article in journal (Refereed) Published
##### Abstract [en]

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

John Wiley & Sons, 2023
##### National Category

Probability Theory and Statistics Discrete Mathematics
##### Identifiers

urn:nbn:se:umu:diva-211151 (URN)10.1112/jlms.12777 (DOI)001010071000001 ()2-s2.0-85162039855 (Scopus ID)
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##### Funder

EU, European Research Council, 101020255
Available from: 2023-07-03 Created: 2023-07-03 Last updated: 2023-12-06Bibliographically approved

Extremal Combinatorics and Probability Group (ECOPRO), Institute for Basic Science (IBS), Daejeon, South Korea.

Mathematics Institute and DIMAP, University of Warwick, Coventry, United Kingdom.

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

School of Mathematics and Statistics, The Open University, Milton Keynes, United Kingdom.

We present a sufficient condition for the stability property of extremal graph problems that can be solved via Zykov's symmetrisation. Our criterion is stated in terms of an analytic limit version of the problem. We show that, for example, it applies to the inducibility problem for an arbitrary complete bipartite graph *B*, which asks for the maximum number of induced copies of *B* in an *n*-vertex graph, and to the inducibility problem for *K*_{2,1,1,1} and *K*_{3,1,1}, the only complete partite graphs on at most five vertices for which the problem was previously open.

Open this publication in new window or tab >>The induced saturation problem for posets### Freschi, Andrea

### Piga, Simón

### Sharifzadeh, Maryam

### Treglown, Andrew

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_some",{id:"formSmash:j_idt204:2:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_2_j_idt208_otherAuthors",{id:"formSmash:j_idt204:2:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_2_j_idt208_otherAuthors",multiple:true}); 2023 (English)In: Combinatorial Theory, E-ISSN 2766-1334, Vol. 3, no 3, article id 9Article in journal (Refereed) Published
##### Abstract [en]

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

eScholarship Publishing, 2023
##### Keywords

Partially ordered sets, saturation, Turán-type problems
##### National Category

Discrete Mathematics
##### Identifiers

urn:nbn:se:umu:diva-219078 (URN)10.5070/C63362792 (DOI)2-s2.0-85180680891 (Scopus ID)
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Available from: 2024-01-11 Created: 2024-01-11 Last updated: 2024-01-11Bibliographically approved

School of Mathematics, University of Birmingham, United Kingdom.

School of Mathematics, University of Birmingham, United Kingdom.

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

School of Mathematics, University of Birmingham, United Kingdom.

For a fixed poset P, a family F of subsets of [n] is induced P-saturated if F does not contain an induced copy of P, but for every subset S of [n] such that S ∉ F, P is an induced subposet of F ∪{S}. The size of the smallest such family F is denoted by sat∗ (n, P). Keszegh, Lemons, Martin, Pálvölgyi and Patkós [Journal of Combinatorial Theory Series A, 2021] proved that there is a dichotomy of behaviour for this parameter: given any poset P, either sat* (n, P) = O(1) or (Formula presented). In this paper we improve this general result showing that either (Formula presented). Our proof makes use of a Turán-type result for digraphs. Curiously, it remains open as to whether our result is essentially best possible or not. On the one hand, a conjecture of Ivan states that for the so-called diamond poset (Formula presented) we have (Formula presented); so if true this conjecture implies our result is tight up to a multi-plicative constant. On the other hand, a conjecture of Keszegh, Lemons, Martin, Pálvölgyi and Patkós states that given any poset P, either sat* (n, P) = O(1) or (Formula presented). We prove that this latter conjecture is true for a certain class of posets P.

Open this publication in new window or tab >>Groups with few maximal sum-free sets### Liu, Hong

### Sharifzadeh, Maryam

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_some",{id:"formSmash:j_idt204:3:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_3_j_idt208_otherAuthors",{id:"formSmash:j_idt204:3:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_3_j_idt208_otherAuthors",multiple:true}); 2021 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 177, article id 105333Article in journal (Refereed) Published
##### Abstract [en]

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

Elsevier, 2021
##### Keywords

Sum-free sets, Abelian group
##### National Category

Discrete Mathematics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-194731 (URN)10.1016/j.jcta.2020.105333 (DOI)000578989800023 ()2-s2.0-85091205275 (Scopus ID)
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##### Funder

EU, Horizon 2020
Available from: 2022-05-16 Created: 2022-05-16 Last updated: 2022-05-16Bibliographically approved

School of Mathematics, University of Birmingham, UK.

A set of integers is sum-free if it does not contain any solution for x+y=z. Answering a question of Cameron and Erdős, Balogh, Liu, Sharifzadeh and Treglown recently proved that the number of maximal sum-free sets in {1,…,n} is Θ(2μ(n)/2), where μ(n) is the size of a largest sum-free set in {1,…,n}. They conjectured that, in contrast to the integer setting, there are abelian groups G having exponentially fewer maximal sum-free sets than 2μ(G)/2, where μ(G) denotes the size of a largest sum-free set in G.

We settle this conjecture affirmatively. In particular, we show that there exists an absolute constant c>0 such that almost all even order abelian groups G have at most 2(1/2−c)μ(G) maximal sum-free sets.

Open this publication in new window or tab >>On the maximum number of integer colourings with forbidden monochromatic sums### Liu, Hong

### Sharifzadeh, Maryam

### Staden, Katherine

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_some",{id:"formSmash:j_idt204:4:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_4_j_idt208_otherAuthors",{id:"formSmash:j_idt204:4:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_4_j_idt208_otherAuthors",multiple:true}); 2021 (English)In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 28, no 1, article id P1.59Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Discrete Mathematics Other Mathematics
##### Identifiers

urn:nbn:se:umu:diva-182051 (URN)10.37236/8824 (DOI)000652332700001 ()2-s2.0-85103005821 (Scopus ID)
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Available from: 2021-04-16 Created: 2021-04-16 Last updated: 2023-09-05Bibliographically approved

Mathematics Institute, University of Warwick, Coventry, United Kingdom.

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

Mathematical Institute, University of Oxford, Oxford, United Kingdom.

Let f(n, r) denote the maximum number of colourings of A ⊆ {1, …, n} with r colours such that each colour class is sum-free. Here, a sum is a subset {x, y, z} such that x + y = z. We show that f(n, 2) = 2⌈n/2⌉, and describe the extremal subsets. Further, using linear optimisation, we asymptotically determine the logarithm of f(n, r) for r ≤ 5. Similar results were obtained by Hán and Jiménez in the setting of finite abelian groups.

Open this publication in new window or tab >>Asymptotic Structure for the Clique Density Theorem### Kim, Jaehoon

### Liu, Hong

### Pikhurko, Oleg

### Sharifzadeh, Maryam

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_some",{id:"formSmash:j_idt204:5:j_idt208:some",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt204_5_j_idt208_otherAuthors",{id:"formSmash:j_idt204:5:j_idt208:otherAuthors",widgetVar:"widget_formSmash_j_idt204_5_j_idt208_otherAuthors",multiple:true}); 2020 (English)In: Discrete Analysis, E-ISSN 2397-3129, article id 19Article in journal (Refereed) Published
##### Abstract [en]

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

Alliance of Diamond Open Access Journals, 2020
##### Keywords

graph limits, graphon, clique density theorem, stability, etc.
##### National Category

Discrete Mathematics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:umu:diva-179067 (URN)10.19086/da.18559 (DOI)000604632200001 ()2-s2.0-85131725601 (Scopus ID)
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##### Funder

EU, Horizon 2020, 752426
##### Note

Korea Advanced Institute of Sciences and Technology, Daejeon, Republic of Korea.

Mathematics Institute and DIMAP, University of Warwick Coventry, UK.

Mathematics Institute and DIMAP, University of Warwick Coventry, UK.

The famous Erdos-Rademacher problem asks for the smallest number of *r*-cliques in a graph with the given number of vertices and edges. Despite decades of active attempts, the asymptotic value of this extremal function for all *r* was determined only recently, by Reiher [Annals of Mathematics, 184 (2016) 683-707]. Here we describe the asymptotic structure of all almost extremal graphs. This task for *r* = 3 was previously accomplished by Pikhurko and Razborov [Combinatorics, Probability and Computing, 26 (2017) 138-160].

Overlay journal.

Available from: 2021-01-26 Created: 2021-01-26 Last updated: 2023-11-30Bibliographically approved