159 citations · 178 across the 33 of their papers we have counts for
7 papers · 1 filter
On pattern avoiding indecomposable permutations
Alice L. L. Gao, Sergey Kitaev, Philip B. Zhang
Comtet introduced the notion of indecomposable permutations in 1972. A permutation is indecomposable if and only if it has no proper prefix which is itself a permutation. Indecompo…
The Local -Polynomials of Cluster Subdivisions Have Only Real Zeros
Philip B. Zhang
Athanasiadis raised the question whether the local -polynomials of type cluster subdivisions have only real zeros. In this paper, we confirm this conjecture and prove the re…
On the real-rootedness of the local -polynomials of edgewise subdivisions
Philip B. Zhang
Athanasiadis conjectured that, for every positive integer , the local -polynomial of the th edgewise subdivision of any simplex has only real zeros. In this paper, based o…
The unimodality of the Ehrhart -polynomial of the chain polytope of the zig-zag poset
Herman Z. Q. Chen, Philip B. Zhang
We prove the unimodality of the Ehrhart -polynomial of the chain polytope of the zig-zag poset, which was conjectured by Kirillov. First, based on a result due to Stanley, we sh…
The Real-rootedness of Generalized Narayana Polynomials
Herman Z. Q. Chen, Arthur L. B. Yang, Philip B. Zhang
In this paper, we prove the real-rootedness of two classes of generalized Narayana polynomials: one arising as the -polynomials of the generalized associahedron associated to th…
On 132-representable Graphs
Alice L. L. Gao, Sergey Kitaev, Philip B. Zhang
A graph is word-representable if there exists a word over the alphabet such that letters and alternate in if and only if is an edge in . Wor…
Kirillov's unimodality conjecture for the rectangular Narayana polynomials
Herman Z. Q. Chen, Arthur L. B. Yang, Philip B. Zhang
In the study of Kostka numbers and Catalan numbers, Kirillov posed a unimodality conjecture for the rectangular Narayana polynomials. We prove that the rectangular Narayana polynom…