Results 21 to 30 of about 125 (122)
Entropic Matroids and Their Representation
Entropy, 2019 This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have support of cardinality p.
Emmanuel Abbe, Sophie Spirkl
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Graphical designs and extremal combinatorics
Linear Algebra and its Applications, 2020 A graphical design is a proper subset of vertices of a graph on which many eigenfunctions of the Laplacian operator have mean value zero. In this paper, we show that extremal independent sets make extremal graphical designs, that is, a design on which the maximum possible number of eigenfunctions have mean value zero.
openaire +5 more sources
An extremal problem on trees and database theory [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We consider an extremal problem on labelled directed trees and applications to database theory. Among others, we will show explicit keysystems on an underlying set of size $n$, that cannot be represented by a database of less than $2^{n(1-c\cdot \log ...
Gyula O.H. Katona, Krisztián Tichler
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Generalized Ramsey–Turán density for cliques
Forum of Mathematics, SigmaWe study the generalized Ramsey–Turán function $\mathrm {RT}(n,K_s,K_t,o(n))$ , which is the maximum possible number of copies of $K_s$ in an n-vertex $K_t$ -free graph with independence number $o(n)$ . The case when $s=2$
Jun Gao +3 more
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Pairwise Intersections and Forbidden Configurations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let $f_m(a,b,c,d)$ denote the maximum size of a family $\mathcal{F}$ of subsets of an $m$-element set for which there is no pair of subsets $A,B \in \mathcal{F}$ with $|A \cap B| \geq a$, $|\bar{A} \cap B| \geq b$, $|A \cap \bar{B}| \geq c$, and $|\bar{A}
Richard P. Anstee, Peter Keevash
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Extremal Permanents of Laplacian Matrices of Unicyclic Graphs
AxiomsThe extremal problem of Laplacian permanents of graphs is a classical and challenging topic in algebraic combinatorics, where the inherent #P-complete complexity of permanent computation renders this pursuit particularly intractable.
Tingzeng Wu +2 more
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A proof of the Elliott–Rödl conjecture on hypertrees in Steiner triple systems
Forum of Mathematics, SigmaHypertrees are linear hypergraphs where every two vertices are connected by a unique path. Elliott and Rödl conjectured that for any given $\mu>0$ , there exists $n_0$ such that the following holds.
Seonghyuk Im +3 more
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Additive energies on discrete cubes
Discrete Analysis, 2023 One definition of additive combinatorics is that it is the study of subsets of (usually Abelian) groups. Two much studied parameters associated with a subset $A$ are the size of its sumset $A+A=\{a+b:a,b\in A\}$ (or the product set $A.A=\{a.b:a,b\in A\}$
Jaume de Dios Pont +3 more
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Forbidden intersection problems for families of linear maps
Discrete Analysis, 2023 Forbidden intersection problems for families of linear maps, Discrete Analysis 2023:19, 32 pp. A central problem in extremal combinatorics is to determine the maximal size of a set system given constraints on the sizes of the sets in the system and on ...
David Ellis, Guy Kindler, Noam Lifshitz
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The power of many: when genetics met yeasts and high‐throughput
Biological Reviews, EarlyView.ABSTRACT In recent years, complex technological capabilities have evolved, driven by the need to solve complex and integrative biological questions through global analyses. New equipment allows the scaling up and automation of processes which previously were carried out on a very limited scale.
Víctor A. Tallada, Víctor Carranco
wiley +1 more source