7 papers
Proof of a Brown-Mol conjecture on subtree roots
Xian'an Jin, Tianlong Ma, Yi Wang
The subtree polynomial of a tree is the generating function that enumerates its subtrees according to their orders. Brown and Mol conjectured that every subtree root of a tree of o…
Connectivity for slice-projections of connected polymatroids
Xiaxia Guan, Xian'an Jin
It is well-known that deleting or contracting any element of a connected matroid always yields at least one connected minor. However, for a connected polymatroid, only two such ele…
A direct proof of well-definedness for the polymatroid Tutte polynomial
Xiaxia Guan, Xian'an Jin
For a polymatroid over , Bernardi, Kálmán and Postnikov [\emph{Adv. Math.} 402 (2022) 108355] introduced the polymatroid Tutte polynomial relying on th…
Coefficients of univariate Tutte polynomials with one variable fixed
Tianlong Ma, Xiaxia Guan, Xian'an Jin +1
It is well known that the 2-variable Tutte polynomial of a graph includes chromatic polynomial and flow polynomial of , i.e. the cases of and . In 2013, Kálmán…
Combinatorial interpretations of Tutte polynomials at the point
Yu Chen, Xian'an Jin, Tianlong Ma
Let be a simple connected graph, and let be the Tutte polynomial of . Motivated by the works in \cite{Ma}, we, in this paper, introduce the even-left spanning f…
A recursive definition for the polymatroid Tutte polynomial
Xiaxia Guan, Xian'an Jin, Weiling Yang
The Tutte polynomial is a significant invariant of graphs and matroids. It is well-known that it has three equivalent definitions: bases expansion, rank generating function, and de…