Xian'an Jin

activity

20222026

most citedOn the maximum local mean order of sub-k-trees of a k-tree

2 citations · 2 across the 10 of their papers we have counts for

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10 papers · 1 filter

math.CO2026

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…

math.CO2026

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…

math.CO2026

Combinatorial interpretations of Tutte polynomials at the point $(2, - 1)$

Yu Chen, Xian'an Jin, Tianlong Ma

Let $G$ be a simple connected graph, and let $T_{G} (x, y)$ be the Tutte polynomial of $G$ . Motivated by the works in \cite{Ma}, we, in this paper, introduce the even-left spanning f…

math.CO2025

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…

math.CO2025

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 $(k + 1)$ -edge connected graph $…

math.CO2025

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 $G$ includes chromatic polynomial and flow polynomial of $G$ , i.e. the cases of $y = 0$ and $x = 0$ . In 2013, Kálmán in…

math.CO2024

A direct proof of well-definedness for the polymatroid Tutte polynomial

Xiaxia Guan, Xian'an Jin

For a polymatroid $P$ over $[n]$ , Bernardi, Kálmán and Postnikov [\emph{Adv. Math.} 402 (2022) 108355] introduced the polymatroid Tutte polynomial $T_{P}$ relying on the…

math.CO2023

Convolution formulas for multivariate arithmetic Tutte polynomials

Tianlong Ma, Xian'an Jin, Weiling Yang

The multivariate arithmetic Tutte polynomial of arithmetic matroids is a generalization of the multivariate Tutte polynomial of matroids. In this note, we give the convolution form…

math.CO2023★ 2 cited

On the maximum local mean order of sub-k-trees of a k-tree

Zhuo Li, Tianlong Ma, Fengming Dong +1

For a k-tree T, a generalization of a tree, the local mean order of sub-k-trees of T is the average order of sub-k-trees of T containing a given k-clique. The problem whether the l…

math.CO2022

Extremal trees with respect to spectral radius of restrictedly weighted adjacency matrices

Ruiling Zheng, Xiaxia Guan, Xian an Jin

For a graph $G = (V, E)$ and $v_{i} \in V$ , denote by $d_{i}$ the degree of vertex $v_{i}$ . Let $f (x, y) > 0$ be a real symmetric function in $x$ and $y$ . The weighted adjacency matrix $…

Proof of a Brown-Mol conjecture on subtree roots

Connectivity for slice-projections of connected polymatroids

Combinatorial interpretations of Tutte polynomials at the point (2,−1)

A recursive definition for the polymatroid Tutte polynomial

On the coefficients of interior and exterior polynomials of polymatroids

Coefficients of univariate Tutte polynomials with one variable fixed

A direct proof of well-definedness for the polymatroid Tutte polynomial

Convolution formulas for multivariate arithmetic Tutte polynomials

On the maximum local mean order of sub-k-trees of a k-tree

Extremal trees with respect to spectral radius of restrictedly weighted adjacency matrices

Combinatorial interpretations of Tutte polynomials at the point $(2, - 1)$