Publications (9)
Transfer Matrices and Ehrhart Theory for Path and Cyclic Block Polytopes
Xinru Jiang, Shuai Yang, Yueming Zhong
We study block polytopes whose variables are divided into equal-size blocks and whose local inequalities bound the total contribution of adjacent blocks. For blocks arranged along…
On Parity Unimodality of -Catalan Polynomials
Guoce Xin, Yueming Zhong
A polynomial is said to be unimodal if . We investigate the unimodality of rational -Catal…
Proving some conjectures on Kekulé numbers for certain benzenoids by using Chebyshev polynomials
Guoce Xin, Yueming Zhong
In chemistry, Cyvin-Gutman enumerates Kekulé numbers for certain benzenoids and record it as on OEIS. This number is exactly the two variable array defined by t…
Magic labelling enumeration on pseudo-line graphs and pseudo-cycle graphs
Guoce Xin, Yueming Zhong, Yangbiao Zhou
Stanley's theorem establishes that for any finite graph , the number of magic labelings with magic sum can be expressed as a sum of two polynomials in . However,…
The constant term algebra of type : the Structure
Guoce Xin, Chen Zhang, Yue Zhou +1
In this paper, we discover a new noncommutative algebra. We refer this algebra as the constant term algebra of type , which is generated by certain constant term operators. We c…
Alternating adjacent-sum polytopes: transfer matrices and Ehrhart series
Xinru Jiang, Suzhen Wen, Yueming Zhong
The paper investigates a family of alternating adjacent‑sum lattice polytopes, deriving explicit transfer‑matrix representations and detailed Ehrhart generating functions, recurren…