Huilan Li

activity

20062026

most citedSupercharacters, symmetric functions in noncommuting variables, and related Hopf algebras

105 citations · 190 across the 13 of their papers we have counts for

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8 papers · 1 filter

math.CO2026

Finite noncommutative coinvariant algebras

Farid Aliniaeifard, Nantel Bergeron, Huilan Li +1

We study quotients of free associative algebras by the two-sided ideals generated by positive-degree symmetric, quasisymmetric, or free quasisymmetric polynomials. Free quasisymmet…

math.CO2026

A Hopf algebra on permutations with a coupling product

Huilan Li, Yishuo Yang, Nantel Bergeron

We define a coupling product and a draw coproduct on permutations and show that they define a graded, connected, cocommutative, free Hopf algebra $KS$ . In characteristic z…

math.CO2016

Rational Catalan polynomials and rank words

Ryan Kaliszewski, Huilan Li

For $m, n$ coprime we introduce a new statistic skip on $(m, n)$ -rational Dyck paths and give a fast way to compute dinv and skip statistics. We also introduce $(m, n)$ -rank words, wh…

math.CO2016

Structure constants for K-theory of Grassmannians, revisited

Huilan Li, Jennifer Morse, Patrick Shields

The problem of computing products of Schubert classes in the cohomology ring can be formulated as the problem of expanding skew Schur polynomials into the basis of ordinary Schur p…

math.CO2014

The $(m, n)$ -rational $q, t$ -Catalan polynomials for $m = 3$ and their $q, t$ -symmetry

Ryan Kaliszewski, Huilan Li

We introduce a new statistic, skip, on rational $(3, n)$ -Dyck paths and define a marked rank word for each path when $n$ is not a multiple of 3. If a triple of valid statistics (are…

math.CO2010★ 105 cited

Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras

Marcelo Aguiar, Carlos Andre, Carolina Benedetti +25

We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a fi…

math.CO2009★ 17 cited

Combinatorial Hopf algebras and Towers of Algebras - Dimension, Quantization, and Functoriality

Nantel Bergeron, Thomas Lam, Huilan Li

Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $⨁_{n \geq 0} A_{n}$ can be endowed with the structure of grad…

math.CO2007★ 17 cited

Combinatorial Hopf algebras and Towers of Algebras