6 papers
Infinite log-concavity of the Taylor coefficients of the Riemann xi-function
Yanxin Liu, Jianxi Mao
The Riemann hypothesis is equivalent to belonging to the Laguerre--Pólya class. Brändén [J. Reine Angew. Math., 2011] proved that if an entire function in the Laguerre--Póly…
Preservation of log-concavity under Hadamard products
Yanxin Liu, Jianxi Mao
For a nonzero real polynomial , let $\W(p)$ denote the numerator of its ordinary generating function. We prove that if the coefficients of both $\W(p)$ and $\W(q)$ are nonnegati…
Pfaffian--Toeplitz identities, Schur positivity, and the -log-convexity of Baxter polynomials
Yanxin Liu, Jianxi Mao
We use the Pfaffian minor summation formula together with Jacobi--Trudi Toeplitz matrices to derive Pfaffian expansions in skew Schur functions. This yields explicit Schur expansio…
Total positivity of transformation matrices for uniform subdivisions
Yanxin Liu, Jianxi Mao
The transformation of the -vector of a finite simplicial complex under an -uniform subdivision is encoded by a transformation matrix. Mu and Welker conjectured that…
Exceptional-point-constrained locking of boundary-sensitive topological transitions in chiral non-Hermitian SSH-type lattices
Huimin Wang, Yanxin Liu, Zhijian Li +1
Topological transitions in non-Hermitian systems are generally boundary sensitive: a point-gap winding transition under periodic boundary condition (PBC) and a non-Bloch bulk real-…
Weighted Dyck paths with special restrictions on the levels of valleys
Yidong Sun, Qianqian Liu, Yanxin Liu
This paper concentrates on the set of weighted Dyck paths of length with special restrictions on the level of valleys. We first give its explicit formula of th…