1. Team Overview

The team's research covers algebraic combinatorics, enumerative combinatorics, graph theory and its applications, and q-series. In recent years, team members have published papers in journals including Journal of Combinatorial Theory, Series A, Journal of Graph Theory, Advances in Applied Mathematics, SIAM Journal on Discrete Mathematics, and European Journal of Combinatorics. Several faculty members have been selected for municipal talent programs in Tianjin, including the Tianjin 131 Innovative Talent Program and the Young Reserve Talent Support Program. Over the past five years, team members have led or participated in a number of research projects, including General Programs and Young Scientists Fund projects supported by the National Natural Science Foundation of China (NSFC).

2. Team Members

3. Representative Publications

4. Representative Research Areas

Research Area I: Unimodality and Related Properties of Combinatorial Polynomials

Unimodality and related positivity properties form an important research direction in combinatorics and are closely connected with analysis, geometry, probability, and optimization. Topics include unimodality, log-concavity and log-convexity of combinatorial sequences; γ-positivity and real-rootedness of univariate polynomials; and stability and the Lorentzian property of multivariate polynomials. The team has established connections between Sturm sequences of univariate polynomials and stable multivariate polynomials, and has systematically studied applications of interlacing and stability methods in combinatorics. This work has resolved conjectures posed by Francesco Brenti, John Stembridge, Christos A. Athanasiadis, Yongnan Ye, and others. Related papers have appeared in Journal of Combinatorial Theory, Series A, Advances in Applied Mathematics, and SIAM Journal on Discrete Mathematics.

Research Area II: Group Connectivity and Flow Theory

Graph coloring and flow theory are central topics in graph theory and have connections with combinatorial optimization, information theory, and related areas. In the 1950s, William Tutte developed nowhere-zero flow theory in the context of the Four Color Problem. In 1992, François Jaeger, Nathan Linial, Charles Payan, and Michael Tarsi introduced group connectivity as an extension of nowhere-zero flow theory to a more general group-valued setting. The team's work focuses mainly on two directions: (1) coloring problems for graphs and hypergraphs, including open problems and conjectures; and (2) group connectivity and related flow problems, including integer flows and modulo orientations. Related results have appeared in Journal of Combinatorial Theory, Series B, Journal of Graph Theory, SIAM Journal on Discrete Mathematics, Theoretical Computer Science, and Journal of Combinatorial Optimization.

Research Area III: Cycle Structures and Spanning Trees

Cycle structure and spanning-tree problems are longstanding topics in structural and extremal graph theory. In recent years, the team has studied Hamiltonian cycles, pancyclicity, and dominating cycles, and the numbers of leaves and branch vertices in spanning trees, primarily using degree and implicit-degree conditions. Related papers have been published in Discrete Mathematics, Discrete Applied Mathematics, and Graphs and Combinatorics.

Research Area IV: Ranks and M₂-Ranks of Overpartitions

In partition theory and the study of q-series, the team has investigated rank differences and M₂-rank differences for overpartitions modulo 4 and 8 and their connections with mock theta functions. Generating functions for rank differences are related to several mock theta functions, while generating functions for M₂-rank differences are related to second-order mock theta functions; these results also yield a number of identities and inequalities. Related papers have appeared in Ramanujan Journal and International Journal of Number Theory. The team has also studied multiparameter generalizations of mock theta functions, their expressions in terms of Appell–Lerch sums, their connections with universal mock theta functions, and radial-limit phenomena. Related papers have appeared in Proceedings of the American Mathematical Society and Journal of Mathematical Analysis and Applications.

Research Area V: Stanley's Shuffle Theorem

Stanley's shuffle theorem originates in R. P. Stanley's 1972 work on P-partitions and describes the joint distribution of the descent number and major index over shuffles of two disjoint permutations. Stanley asked for a proof avoiding the q-Pfaff–Saalschütz identity, and bijective proofs were later given by Goulden and Stadler. The team has developed a new explicit bijective proof using the insertion lemma of Haglund, Loehr, and Remmel and, based on this combinatorial construction, established several refinements and related applications. Relevant papers have appeared in Journal of Combinatorial Theory, Series A, European Journal of Combinatorics, and Electronic Journal of Combinatorics.

5. Graduate Admissions

Students interested in the Combinatorics and Graph Theory Research Team are welcome to apply.

The team admits approximately 4–5 master's students each year.