Results 41 to 50 of about 887,124 (211)
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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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 words in morphic subshifts [PDF]
, 2013 Given an infinite word X over an alphabet A a letter b occurring in X, and a total order \sigma on A, we call the smallest word with respect to \sigma starting with b in the shift orbit closure of X an extremal word of X.
Currie, James D. +3 more
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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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On the extremal combinatorics of the hamming space
Journal of Combinatorial Theory, Series A, 1995 In \(n\)-dimensional Hamming space three points are on a line, if they satisfy the triangle inequality with equality. The paper introduces the following problem: How many different points can be found in the Hamming space so that no three of them are on a line (that is they are in general position)? This maximum value is \(A(n)\). The paper surveys the
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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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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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Shattered Sets and the Hilbert Function [PDF]
, 2016 We study complexity measures on subsets of the boolean hypercube and exhibit connections between algebra (the Hilbert function) and combinatorics (VC theory). These connections yield results in both directions.
Moran, Shay, Rashtchian, Cyrus
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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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Extremes of the internal energy of the Potts model on cubic graphs [PDF]
, 2017 We prove tight upper and lower bounds on the internal energy per particle (expected number of monochromatic edges per vertex) in the anti-ferromagnetic Potts model on cubic graphs at every temperature and for all $q \ge 2$.
Davies, Ewan +3 more
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