1 citations · 1 across the 11 of their papers we have counts for
15 papers
Alternating Hamilton Paths and Cycles in Poset Products
Yuxian Dong, Jianxi Mao
We study alternating Hamilton paths and cycles in the comparability graphs of finite posets. We prove that if a finite poset with at least two elements admits an alternating Ha…
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…
Proof of Fishburn's latent-subset conjecture
Yuxian Dong, Jianxi Mao
Fishburn's latent-subset conjecture, proposed in 1987 and revisited in 1988, asserts that for every dual intersecting family , there exists s…
Interlacing on the Unit Circle via Coefficientwise Reciprocals
Jianxi Mao, Lijie Wang, Sainan Zheng
Let be a polynomial with positive coefficients, and define its coefficientwise reciprocal by It is known that…
Proof of Almkvist's conjecture on the unimodality of partition polynomials
Jianxi Mao, Wenle Shi, Bao-xuan Zhu
For integers and , let The coefficient of in \(F_{r,n}(q)\) counts partitions of into parts at most…
Eulerian triangle is totally positive of order 3
Jianxi Mao
Brenti conjectured that the Eulerian triangle is totally positive. In this paper, we prove that the Eulerian triangle is totally positive of order 3, thereby providing a partial af…
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…
Engel's Interval Packing Problem in the Boolean Lattice
Yuxian Dong, Jianxi Mao
Let \(\mathcal{B}_n\) be the Boolean lattice of all subsets of \([n]\) and let \(\mathcal{P}_{n;\ell,u}\) be the subposet of \(\mathcal{B}_n\) induced by the consecutive levels \(\…
The analytic properties of Hoggatt triangles
Jianxi Mao, Wenle Shi
The -Hoggatt triangle is a lower triangular matrix whose entries are given by specific minors of Pascal's triangle formed by consecutive rows and columns. The cases $d=1…
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…
The Narayana transformation
Jianxi Mao, Lijie Wang
For , let \[ N_{n,m}(x)={}_2F_1(-n,-n-m;m+1;x), \] which specializes to the Narayana polynomials of types and for and , respectively. We…
Yet another criterion for the total positivity of Riordan arrays
Jianxi Mao, Lili Mu, Yi Wang
Let be a Riordan array, where and . We show that if the matrix \begin{equation*} \left[\begin{array}…
Equidistributions around special kinds of descents and excedances
Bin Han, Jianxi Mao, Jiang Zeng
We consider a sequence of four variable polynomials by refining Stieltjes' continued fraction for Eulerian polynomials. Using combinatorial theory of Jacobi-type continued fraction…
Further equidistribution of set-valued statistics on permutations
Jianxi Mao, Jiang Zeng
We construct bijections to show that two pairs of sextuple set-valued statistics of permutations are equidistributed on symmetric groups. This extends a recent result of Sokal and…
Eulerian polynomials and excedance statistics
Bin Han, Jianxi Mao, Jiang Zeng
A formula of Stembridge states that the permutation peak polynomials and descent polynomials are connected via a quadratique transformation. The aim of this paper is to establish t…