Results 51 to 60 of about 887,803 (201)
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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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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Gowers norms for automatic sequences
Discrete Analysis, 2023 Gowers norms for automatic sequences, Discrete Analysis 2023:4, 62 pp. There are several situations in additive and extremal combinatorics where it is useful to decompose an object $X$ into a "structured" part $S(X)$ and a "quasirandom" part $Q(X)$.
Jakub Byszewski +2 more
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Discrete Analysis, 2020 An efficient container lemma, Discrete Analysis 2020:17, 56 pp. The hypergraph container lemma, discovered independently in 2012 by David Saxton and Andrew Thomason, and by József Balogh, Robert Morris and Wojciech Samotij, is an extremely powerful tool
Jozsef Balogh, Wojciech Samotij
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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
openaire +3 more sources
A complex network perspective on brain disease
Biological Reviews, EarlyView.ABSTRACT If brain anatomy and dynamics have a complex network structure as it has become standard to posit, it is reasonable to assume that such a structure should play a key role not only in brain function but also in brain dysfunction. However, exactly how network structure is implicated in brain damage and whether at least some pathologies can be ...
David Papo, Javier M. Buldú
wiley +1 more source
Simple juntas for shifted families
Discrete Analysis, 2020 **For the moment the link is to the submitted version of the article. It will be updated when the final version has been posted to arXiv.** Simple juntas for shifted families, Discrete Analysis 2020:14, 18 pp.
Peter Frankl, Andrey Kupavskii
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The Necessary Uniformity of Physical Probability
Philosophy and Phenomenological Research, EarlyView.ABSTRACT According to contemporary consensus, physical probabilities may be “non‐uniform”: they need not correspond to a uniform measure over the space of physically possible worlds. Against consensus, I argue that only uniform probabilities connect robustly to long‐run frequencies.
Ezra Rubenstein
wiley +1 more source
Further results on permanents of Laplacian matrices of trees
Open MathematicsThe research on the permanents of graph matrices is one of the contemporary research topic in algebraic combinatorics. Brualdi and Goldwasser characterized the upper and lower bounds of permanents of Laplacian matrices of trees.
Wu Tingzeng, Dong Xiangshuai
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