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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some conjectures on real-rootedness
实根性 组合数学 大群多项式
2023/4/21
The real-rootedness has been drawing attention of many mathematicians to study them on a large group of polynomials in Combinatorics. This talk is concerned with some conjectures on the real-rootednes...
Branden's Conjectures on the Boros-Moll Polynomials
Boros-Moll Polynomials Real-rootedness Sturm sequence, 3-log-concavity
2012/5/24
We prove two conjectures of Br\"{a}nd\'{e}n on the real-rootedness of polynomials $Q_n(x)$ and $R_n(x)$ which are related to the Boros-Moll polynomials $P_n(x)$. In fact, we show that both $Q_n(x)$ an...
Chromatic number, clique subdivisions, and the conjectures of Hajos and Erdos-Fajtlowicz
Chromatic number clique subdivisions Hajos and Erdos-Fajtlowicz Combinatorics
2011/9/1
Abstract: For a graph $G$, let $\chi(G)$ denote its chromatic number and $\sigma(G)$ denote the order of the largest clique subdivision in $G$. Let H(n) be the maximum of $\chi(G)/\sigma(G)$ over all ...
Large matchings in uniform hypergraphs and the conjectures of Erdos and Samuels
Large matchings uniform hypergraphs conjectures of Erdos and Samuels Combinatorics Probability
2011/8/26
Abstract: In this paper we study conditions which guarantee the existence of perfect matchings and perfect fractional matchings in uniform hypergraphs. We reduce this problem to an old conjecture by E...
Conjectures of Alperin and Broue for 2-blocks with elementary abelian defect groups of order 8
Conjectures of Alperin Broue for 2-blocks elementary abelian defect groups of order 8
2011/2/21
Using the classification of finite simple groups, we prove Alperin’s weight conjecture
and the character theoretic version of Brou´e’s abelian defect conjecture for 2-blocks of finite groups wi...