Zobrazeno 1 - 10
of 30
pro vyhledávání: '"05C65, 05D05"'
We present a general method to modify existing uniquely decodable codes in the $T$-user binary adder channel. If at least one of the original constituent codes does not have average weight exactly half of the dimension, then our method produces a new
Externí odkaz:
http://arxiv.org/abs/2312.11723
Autor:
Balogh, József, Luo, Haoran
Denote by $\mathcal{C}^-_{\ell}$ the $3$-uniform hypergraph obtained by removing one hyperedge from the tight cycle on $\ell$ vertices. It is conjectured that the Tur\'an density of $\mathcal{C}^-_{5}$ is $1/4$. In this paper, we make progress toward
Externí odkaz:
http://arxiv.org/abs/2303.10530
Autor:
Mofidi, Alireza
Publikováno v:
Discrete Applied Mathematics, 283 (2020) 207-230
Well-graded families, extremal systems and maximum systems (the last two in the sense of VC-theory and Sauer-Shelah lemma on VC-dimension) are three important classes of set systems. This paper aims to study the notion of duality in the context of th
Externí odkaz:
http://arxiv.org/abs/2212.08373
Autor:
Kirsch, Rachel, Radcliffe, Jamie
Publikováno v:
SIAM Journal on Discrete Mathematics, Volume 37, Issue 3 (2023), pages 1436-1456
Recently Chase determined the maximum possible number of cliques of size $t$ in a graph on $n$ vertices with given maximum degree. Soon afterward, Chakraborti and Chen answered the version of this question in which we ask that the graph have $m$ edge
Externí odkaz:
http://arxiv.org/abs/2207.02336
Autor:
Zhou, Junling, Zhou, Wenling
Various kinds of fingerprinting codes and their related combinatorial structures are extensively studied for protecting copyrighted materials. This paper concentrates on one specialised fingerprinting code named wide-sense frameproof codes in order t
Externí odkaz:
http://arxiv.org/abs/2002.11266
One powerful method for upper-bounding the largest independent set in a graph is the Hoffman bound, which gives an upper bound on the largest independent set of a graph in terms of its eigenvalues. It is easily seen that the Hoffman bound is sharp on
Externí odkaz:
http://arxiv.org/abs/1911.02297
Autor:
Lei, Hui, Lu, Linyuan
Frankl and F\"uredi conjectured in 1989 that the maximum Lagrangian, denoted by $\lambda_r(m)$, among all $r$-uniform hypergraphs of fixed size $m$ is achieved by the minimum hypergraph $C_{r,m}$ under the colexicographic order. We say $m$ in {\em pr
Externí odkaz:
http://arxiv.org/abs/1806.11259
Frankl and F\"uredi conjectured in 1989 that the maximum Lagrangian of all $r$-uniform hypergraphs of fixed size $m$ is realized by the minimum hypergraph $C_{r,m}$ under the colexicographic order. In this paper, we prove a weaker version of the Fran
Externí odkaz:
http://arxiv.org/abs/1806.10846
Autor:
Bellmann, Louis, Reiher, Christian
Publikováno v:
Combinatorica 39 (2019), no. 5, 961--982
Confirming a conjecture of Vera T. S\'os in a very strong sense, we give a complete solution to Tur\'an's hypergraph problem for the Fano plane. That is we prove for $n\ge 8$ that among all $3$-uniform hypergraphs on $n$ vertices not containing the F
Externí odkaz:
http://arxiv.org/abs/1804.07673
Publikováno v:
Journal of Combinatorial Theory, Series A 160 (2018), 111-135
We show that for an infinitely many natural numbers $k$ there are $k$-uniform hypergraphs which admit a `rescaling phenomenon' as described in [9]. More precisely, let $\mathcal{A}(k,I, n)$ denote the class of $k$-graphs on $n$ vertices in which the
Externí odkaz:
http://arxiv.org/abs/1707.01930