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Sharifzadeh, Maryam
Publications (6 of 6) Show all publications
Garbe, F., Hancock, R., Hladký, J. & Sharifzadeh, M. (2023). Limits of latin squares. Discrete Analysis, 2023, Article ID 8.
Open this publication in new window or tab >>Limits of latin squares
2023 (English)In: Discrete Analysis, E-ISSN 2397-3129, Vol. 2023, article id 8Article in journal (Refereed) Published
Abstract [en]

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.

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)
Funder
EU, Horizon 2020, 648509EU, Horizon 2020, 752426
Note

Overlay journal.

Available from: 2023-11-30 Created: 2023-11-30 Last updated: 2024-01-08Bibliographically approved
Liu, H., Pikhurko, O., Sharifzadeh, M. & Staden, K. (2023). Stability from graph symmetrisation arguments with applications to inducibility. Journal of the London Mathematical Society, 108(3), 1121-1162
Open this publication in new window or tab >>Stability from graph symmetrisation arguments with applications to inducibility
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]

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 K2,1,1,1 and K3,1,1, the only complete partite graphs on at most five vertices for which the problem was previously open.

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)
Funder
EU, European Research Council, 101020255
Available from: 2023-07-03 Created: 2023-07-03 Last updated: 2023-12-06Bibliographically approved
Freschi, A., Piga, S., Sharifzadeh, M. & Treglown, A. (2023). The induced saturation problem for posets. Combinatorial Theory, 3(3), Article ID 9.
Open this publication in new window or tab >>The induced saturation problem for posets
2023 (English)In: Combinatorial Theory, E-ISSN 2766-1334, Vol. 3, no 3, article id 9Article in journal (Refereed) Published
Abstract [en]

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.

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)
Available from: 2024-01-11 Created: 2024-01-11 Last updated: 2024-01-11Bibliographically approved
Liu, H. & Sharifzadeh, M. (2021). Groups with few maximal sum-free sets. Journal of combinatorial theory. Series A (Print), 177, Article ID 105333.
Open this publication in new window or tab >>Groups with few maximal sum-free sets
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]

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.

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)
Funder
EU, Horizon 2020
Available from: 2022-05-16 Created: 2022-05-16 Last updated: 2022-05-16Bibliographically approved
Liu, H., Sharifzadeh, M. & Staden, K. (2021). On the maximum number of integer colourings with forbidden monochromatic sums. The Electronic Journal of Combinatorics, 28(1), Article ID P1.59.
Open this publication in new window or tab >>On the maximum number of integer colourings with forbidden monochromatic sums
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]

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.

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)
Available from: 2021-04-16 Created: 2021-04-16 Last updated: 2023-09-05Bibliographically approved
Kim, J., Liu, H., Pikhurko, O. & Sharifzadeh, M. (2020). Asymptotic Structure for the Clique Density Theorem. Discrete Analysis, Article ID 19.
Open this publication in new window or tab >>Asymptotic Structure for the Clique Density Theorem
2020 (English)In: Discrete Analysis, E-ISSN 2397-3129, article id 19Article in journal (Refereed) Published
Abstract [en]

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].

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)
Funder
EU, Horizon 2020, 752426
Note

Overlay journal. 

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