Research Interest
My research area is
enumerative combinatorics and
algebraic combinatorics.
The field of algebraic combinatorics is interested in analyzing algebraic structures using combinatorial methods such as generating functions, bijections, etc.
My primary interest in algebraic combinatorics is the combinatorics of
symmetric functions
and
Macdonald polynomials
, with a focus on the Rational Shuffle Conjecture and the Delta Conjecture, which study the relations between combinatorial objects such as parking functions and the Frobenius Characteristic of some algebraic structures such as diagonal harmonics. They are also natural generalizations of the $(q,t)$-Catalan combinatorics.
The field of enumerative combinatorics deals with counting combinatorial objects. My primary interests in enumerative combinatorics are permutation patterns and ordered set partition enumerations.
Funding
NSFC Grant (12001037):
Combinatorial Problems Derived from the Shuffle Conjecture.
Publications
- Pattern-Avoidance and Fuss–Catalan Numbers
[with Per Alexandersson, Frether Kebede and Samuel Fufa] (Journal of Integer Sequences, 26, 2023) [pdf]
- Schur function expansions and the Rational Shuffle Theorem
[with Jeff Remmel] (Journal of Combinatorial Theory, Series A, 175, 2020) [pdf]
- The valley version of the Extended Delta Conjecture [with Andy Wilson]
(Journal of Combinatorial Theory, Series A, 175, 2020) [pdf]
- $e$-positivity results and conjectures [with Adriano Garsia, Jim Haglund and Marino Romero] (arXiv, 2019) [pdf]
- Patterns in words of ordered set partitions [with Jeff Remmel] (Journal of Combinatorics, 10 (3), 2019) [pdf]
The original version also discussed pattern avoidance in parking functions [pdf]
- Classical pattern distributions in $\mathcal{S}_n(132)$ and $\mathcal{S}_n(123)$ [with Jeff Remmel] (Discrete Mathematics & Theoretical Computer Science, 21 (2)， 2019) [pdf]
- Counting Consecutive Pattern Matches in $\mathcal{S}_n(132)$ and $\mathcal{S}_n(123)$ [with Ran Pan and Jeff Remmel] (Advances in Applied Mathematics, 105, 2018) [pdf]
- Schur Function Expansions and the Rational Shuffle Conjecture [with Jeff Remmel]
Extended abstract appear in Proceedings of FPSAC 2017, (Seminaire Lotharingien de Combinatoire, 78B, 2017) [pdf]
- On the Schur positivity of $Δ_{e_2} e_n[X]$ [with Jeff Remmel, Emily Sergel and Guoce Xin] (Electronic Journal of Combinatorics, 25 (4), 2018) [pdf]
- Quadrant marked mesh patterns in 123-avoiding permutations [with Jeff Remmel] (Discrete Mathematics & Theoretical Computer Science, 19 (2), 2018) [pdf]
Talks
- (2023.4) Peak distributions and peak maps in lattice paths, Seminar on Combinatorics, Chinese Academy of Sciences, Beijing, China
- (2021.4) Exploring a combinatorial model of Stanley’s e-positive conjecture,
Workshop on Combinatorics, Algebra and Geometry, Nankai University, Tianjin, China,
5th Conference on Combinatorics and Symbolic Computation,
Zhejiang Normal University, Zhejiang, China
- (2020.11) q-unimodality of parking function polynomials,
5th Conference on Combinatorics and Symbolic Computation,
Zhejiang Normal University, Zhejiang, China
- (2020.7) Bijectivity Problems in Parking Functions, 2020 Workshop on Algebraic Combinatorics, Sichuan University, Sichuan, China
- (2020.6) Mod $k$-alternating permutations in $\mathcal{S}_{n}(132)$, Permutation Patterns Virtual Workshop 2020, Valparaiso University, IN, USA
- (2019.5) Some conjectures about column LLT polynomials, UC Davis Algebraic Geometry Seminar, UC Davis, Davis, CA, USA
- (2019.1) Counting classical patterns in $\mathcal{S}_n(132)$ and $\mathcal{S}_n(123)$, UCLA Combinatorics Seminar, UCLA, Los Angeles, CA, USA [website] [pdf]
- (2018.7)
Classical permutation distribution in $\mathcal{S}_n(132)$ and $\mathcal{S}_n(123)$,
Permutation Patterns 2018, Hanover, NH, USA
[website]
[pdf]
- (2018.7) Combinatorial Problems in Dyck paths and Parking Functions,
Center for Combinatorics Seminar, Nankai University, Tianjin, China [website] [pdf]
- (2018.3)
Conjectures for the delta operator expression $\Delta'_{e_k}\Delta_{h_r}e_n$,
The CAGE Seminar, University of Pennsylvania, Philadelphia, PA, USA [website] [pdf]
- (2018.1)
Conjectures for $\Delta'_{e_k}\Delta_{h_r}e_n$,
LaCIM, Université du Québec à Montréal, Montréal, Canada
[website] [pdf]
- (2017.8)
Special Cases in the Combinatorics of Rational Shuffle Conjecture,
Center for Combinatorics Seminar, Nankai University, Tianjin, China [website] [pdf]
- (2016.6) Patterns in Ordered Set Partitions and
Parking Functions,
Permutation Patterns 2016, Washington D.C., USA
[website] [pdf]
- (2016.5) Rational Shuffle Conjecture When $n = 3$ or $m = 3$, UC San Diego, La Jolla, USA
[website] [pdf]
Posters
- (2017.7) Schur Function Expansions and the Rational
Shuffle Conjecture,
FPSAC 2017, London, UK [website]
- (2017.6) Quadrant marked mesh patterns in $123$-avoiding permutations,
Permutation Patterns 2017, Reykjavik, Iceland [website]
Other Conferences
- (2019.1) Representation Theory Connections to (q,t)-Combinatorics, Banff, Canada [website]
- (2018.7) FPSAC 2018, Hanover, NH, USA [website]
