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math.CO2024
On -Coefficient Binomial Polynomiality of Hurwitz Numbers and Generalized Dessin Counting
Zhiyuan Wang, Chenglang Yang
In this paper, we study a certain type of Hurwitz numbers which count branched covers over the Riemann sphere admitting several branch points with fixed ramification types, one bra…
math.CO2024
Schröder Paths, Their Generalizations and Knot Invariants
Ce Ji, Qian Tang, Chenglang Yang
We study some kinds of generalizations of Schröder paths below a line with rational slope and derive the -difference equations that are satisfied by their generating functions.…
math.CO2024
Hook-Lengths, Symplectic/Orthogonal Contents and Amdeberhan's Conjectures
Chenglang Yang
The symplectic/orthogonal contents of partitions are related to the dimensions of irreducible representations of symplectic/orthogonal groups. In 2012, motivated by Nekrasov--Okoun…