159 citations · 178 across the 33 of their papers we have counts for
8 papers · 1 filter
Zeros and interlacing for multiset Eulerian-Narayana polynomials
Philip B. Zhang, Tongyuan Zhao
We prove the real-rootedness conjecture of Lin, Ma, Ma, and Zhou (2021) for multiset Eulerian-Narayana polynomials, including simplicity and negativity of all zeros after removing…
Infinite log-concavity of the Boros--Moll sequences
Matthew H. Y. Xie, Philip B. Zhang
Let be the Boros--Moll coefficient sequence. We prove that, for every integer , the polynomial \[ M_n(x)=\sum_{i=0}^n \bigl(d_i(n)^2-d_{i-1}(n)d_{i+1}(n)\…
Real-rootedness of the -polynomials of sparse paving matroids and strict interlacing for uniform matroids
Matthew H. Y. Xie, Philip B. Zhang
We prove that the -polynomial of every sparse paving matroid has only negative real zeros, confirming the real-rootedness conjecture of Proudfoot, Xu, and Young for this class.…
Real-rootedness of the -polynomial under graph joins
Mingyang Kang, Zhixin Liu, Sophie C. C. Sun +1
For a simple graph with vertices, write its chromatic polynomial in the rising factorial basis as where $ \lan…
Normalized skew Schur polynomials are Lorentzian
Philip B. Zhang
We prove the conjecture of Huh, Matherne, Mészáros, and St.~Dizier that the normalization of every skew Schur polynomial in finitely many variables is Lorentzian. We first realize…
Real-rootedness of Kazhdan--Lusztig and -polynomials of thagomizer matroids and graphic matroids of
Philip B. Zhang
Let , and let denote the Kazhdan--Lusztig polynomial of its graphic matroid. We prove that, whenever and , the polynomial …
Simultaneous avoidance of length-4 patterns in ascent sequences
Qi Liu, Sergey Kitaev, Philip B. Zhang
Ascent sequences form a central class of combinatorial objects, as they are in bijection with several important families such as (2+2)-free posets, Stoimenow matchings, and other F…
Equivariant Kazhdan--Lusztig Polynomials of Thagomizer Matroids with a Hyperoctahedral Group Action
Matthew H. Y. Xie, Philip B. Zhang, Michael X. X. Zhong
The thagomizer matroid, realized as the graphic matroid of the complete tripartite graph , has full automorphism group isomorphic to the hyperoctahedral group whenever $…