16 citations · 53 across the 29 of their papers we have counts for
29 papers
Moments for generalizations of a coin flip game
Jia Huang
We derive a recursive formula for the moments of the number of flips using a possibly biased coin to produce a prescribed finite binary string when is either a run of heads…
Dimensions of compositions modulo a prime
Jia Huang
The (ordinary) representation theory of the symmetric group is fascinating and has rich connections to combinatorics, including the Frobenius correspondence to the self-dual graded…
A coin flip game and generalizations of Fibonacci numbers
Jia Huang
We study a game in which one keeps flipping a coin until a given finite string of heads and tails occurs. We find the expected number of coin flips to end the game when the ending…
Even and odd compositions with restricted parts
Jia Huang
A result of Legendre asserts that the difference between the numbers of (length) even and odd partitions of into distinct parts is , , or ; this also follows from Eul…
Associative-commutative spectra for some varieties of groupoids
Jia Huang, Erkko Lehtonen
The associative spectrum of a groupoid (i.e., a set with a binary operation) measures its nonassociativity while the associative-commutative spectrum measures both nonassociativity…
Partially Palindromic Compositions
Jia Huang
We generalize recent work of Andrews, Just, and Simay on modular palindromic compositions and anti-palindromic compositions by viewing all compositions partially (modular) palindro…
Domination ratio of a family of integer distance digraphs with arbitrary degree
Jia Huang
An integer distance digraph is the Cayley graph of the additive group of all integers with respect to a finite subset . The dom…
The associative-commutative spectrum of a binary operation
Jia Huang, Erkko Lehtonen
We initiate the study of a quantitative measure for the failure of a binary operation to be commutative and associative. We call this measure the associative-commutative spectrum a…
Norton algebras of the Hamming Graphs via linear characters
Jia Huang
The Norton product is defined on each eigenspace of a distance regular graph by the orthogonal projection of the entry-wise product. The resulting algebra, known as the Norton alge…
New upper bounds for the bondage number of a graph in terms of its maximum degree and Euler characteristic
Jia Huang, Jian Shen
The bondage number of a graph is the smallest number of edges whose removal from results in a graph with larger domination number. Let be embeddable on a surface…
Nonassociativity of the Norton Algebras of some distance regular graphs
Jia Huang
A Norton algebra is an eigenspace of a distance regular graph endowed with a commutative nonassociative product called the Norton product, which is defined as the projection of the…
Domination ratio of integer distance digraphs
Jia Huang
An integer distance digraph is the Cayley graph of the additive group of all integers with respect to some finite subset . Th…
Hecke algebras of simply-laced type with independent parameters
Jia Huang
We study the (complex) Hecke algebra of a finite simply-laced Coxeter system with independent parameters $\mathbf{q} \in \left( \mathbb{C} \setm…
Compositions with restricted parts
Jia Huang
Euler showed that the number of partitions of into distinct parts equals the number of partitions of into odd parts. This theorem was generalized by Glaisher and further by…
Variations of the Catalan numbers from some nonassociative binary operations
Nickolas Hein, Jia Huang
We investigate certain nonassociative binary operations that satisfy a four-parameter generalization of the associative law. From this we obtain variations of the ubiquitous Catala…
The Nonassociativity of the Double Minus Operation
Jia Huang, Madison Mickey, Jianbai Xu
The sequence A000975 in OEIS can be defined by , if is odd, and if is even. This sequence satisfies other recurrence relations, admit…
Hall-Littlewood polynomials and a Hecke action on ordered set partitions
Jia Huang, Brendon Rhoades, Travis Scrimshaw
We construct an action of the Hecke algebra on a quotient of the polynomial ring , where . The dimension of our quotient ring is the…
Critical groups for Hopf algebra modules
Darij Grinberg, Jia Huang, Victor Reiner
This paper considers an invariant of modules over a finite-dimensional Hopf algebra, called the critical group. This generalizes the critical groups of complex finite group represe…
Ordered set partitions and the 0-Hecke algebra
Jia Huang, Brendon Rhoades
Let the symmetric group act on the polynomial ring by variable permutation. The coinvariant algebra is the…
Modular Catalan Numbers
Nickolas Hein, Jia Huang
The Catalan number enumerates parenthesizations of where is a binary operation. We introduce the modular Catalan number to count equivalence cl…
Absolute order in general linear groups
Jia Huang, Joel Brewster Lewis, Victor Reiner
This paper studies a partial order on the general linear group GL(V) called the absolute order, derived from viewing GL(V) as a group generated by reflections, that is, elements wh…
A uniform generalization of some combinatorial Hopf algebras
Jia Huang
We generalize the Hopf algebras of free quasisymmetric functions, quasisymmetric functions, noncommutative symmetric functions, and symmetric functions to certain representations o…
A tableau approach to the representation theory of 0-Hecke algebras
Jia Huang
A 0-Hecke algebra is a deformation of the group algebra of a Coxeter group. Based on work of Norton and Krob--Thibon, we introduce a tableau approach to the representation theory o…
Hecke algebras with independent parameters
Jia Huang
We study the Hecke algebra $\H(\bq)$ over an arbitrary field $\FF$ of a Coxeter system with independent parameters $\bq=(q_s\in\FF:s\in S)$ for all generators. This algebra…