4 papers
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…