5 papers
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…
A deletion-contraction formula and monotonicity properties for the polymatroid Tutte polynomial
Xiaxia Guan, Xian'an Jin, Tamás Kálmán
The Tutte polynomial is a fundamental invariant of matroids. The polymatroid Tutte polynomial , introduced by Bernardi, Kálmán, and Postnikov, is an extensi…
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…
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…
On the coefficients of interior and exterior polynomials of polymatroids
Xiaxia Guan, Xian'an Jin, Tianlong Ma +1
The Tutte polynomial is an important invariant of graphs and matroids. Chen and Guo \emph{[Adv. in Appl. Math. 166 (2025) 102868.]} proved that for a -edge connected graph $…