105 citations · 190 across the 13 of their papers we have counts for
14 papers
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…
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 . In characteristic z…
An Approach for Thyroid Nodule Analysis Using Thermographic Images
J. R. González, É. O. Rodrigues, C. P. Damião +6
Thyroid cancer is said to be the second most common type of cancer in female individuals and the third in males by 2030, according to projections. In general, detecting cancer in i…
Rational Catalan polynomials and rank words
Ryan Kaliszewski, Huilan Li
For coprime we introduce a new statistic skip on -rational Dyck paths and give a fast way to compute dinv and skip statistics. We also introduce -rank words, wh…
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…
The -rational -Catalan polynomials for and their -symmetry
Ryan Kaliszewski, Huilan Li
We introduce a new statistic, skip, on rational -Dyck paths and define a marked rank word for each path when is not a multiple of 3. If a triple of valid statistics (are…
Rational Convolution Roots of Isobaric Polynomials
Aura Conci, Huilan Li, Trueman MacHenry
In this paper, we exhibit two matrix representations of the rational roots of generalized Fibonacci polynomials (GFPs) under convolution product, in terms of determinants and perma…
Permanents, Determinants, Weighted Isobaric Polynomials and Integer Sequences
Huilan Li, Trueman MacHenry
In this paper we construct two types of Hessenberg matrices with the properties that every weighted isobaric polynomial (WIP) appears as a determinant of one of them, and as the pe…
The Convolution Ring of Arithmetic Functions and Symmetric Polynomials
Huilan Li, Trueman MacHenry
Inspired by Rearick (1968), we introduce two new operators, LOG and EXP. The LOG operates on generalized Fibonacci polynomials giving generalized Lucas polynomials. The EXP is the…
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…
Non-commutative Combinatorial Inverse Systems
J. -C. Aval, N. Bergeron, H. Li
We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and resul…
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 can be endowed with the structure of grad…
Combinatorial Hopf algebras and Towers of Algebras
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 can be endowed with the structure of grad…
Algebraic Structures on Grothendieck Groups of a Tower of Algebras
Nantel Bergeron, Huilan Li
The Grothendieck group of the tower of symmetric group algebras has a self-dual graded Hopf algebra structure. Inspired by this, we introduce by way of axioms, a general notion of…