105 citations · 633 across the 54 of their papers we have counts for
51 papers · 1 filter
Rook characters as symmetric functions
Rosa Orellana, Alexander N. Wilson, Mike Zabrocki
We give several characterizations of an inhomogeneous basis of the ring of symmetric functions whose evaluations are the character values of the irreducible representations of the…
A geometric and generating function approach to plethysm
Álvaro Gutiérrez, Rosa Orellana, Franco Saliola +2
Plethysm coefficients are the structure coefficients of the plethysm of Schur functions . We study a bivariate gener…
When are Hopf algebras determined by integer sequences?
Nicolas Andrews, Lucas Gagnon, Félix Gélinas +2
We study the category of graded Hopf algebras that are free noncommutative, cocommutative, graded and connected from the perspective of the sequences of dimensions of the graded pi…
The lattice of submonoids of the uniform block permutations containing the symmetric group
Rosa Orellana, Franco Saliola, Anne Schilling +1
We study the lattice of submonoids of the uniform block permutation monoid containing the symmetric group (which is its group of units). We prove that this lattice is distributive…
From quasi-symmetric to Schur expansions with applications to symmetric chain decompositions and plethysm
Rosa Orellana, Franco Saliola, Anne Schilling +1
It is an important problem in algebraic combinatorics to deduce the Schur function expansion of a symmetric function whose expansion in terms of the fundamental quasisymmetric func…
The mystery of plethysm coefficients
Laura Colmenarejo, Rosa Orellana, Franco Saliola +2
Composing two representations of the general linear groups gives rise to Littlewood's (outer) plethysm. On the level of characters, this poses the question of finding the Schur exp…
Quasisymmetric harmonics of the exterior algebra
Nantel Bergeron, Kelvin Chan, Farhad Soltani +1
We study the ring of quasisymmetric polynomials in anticommuting (fermionic) variables. Let denote the polynomials in anticommuting variables. The main results of thi…
A basis for the Diagonal Harmonic Alternants
Adriano Garsia, Mike Zabrocki
It will be shown here that there are differential operators and for each , acting on Diagonal Harmonics, yielding that is a representation of …
Plethysm and the algebra of uniform block permutations
Rosa Orellana, Franco Saliola, Anne Schilling +1
We study the representation theory of the uniform block permutation algebra in the context of the representation theory of factorizable inverse monoids. The uniform block permutati…
Howe duality of the symmetric group and a multiset partition algebra
Rosa Orellana, Mike Zabrocki
We introduce the multiset partition algebra, , that has bases elements indexed by multiset partitions, where is an indeterminate and and are non-ne…
A positivity conjecture on the structure constants of shifted Jack functions
Per Alexandersson, Valentin Féray
We consider Jack polynomials and their shifted analogue $J^#_λ$. In 1989, Stanley conjectured that is a polynomial with nonnegative coefficients…
A combinatorial model for the decomposition of multivariate polynomial rings as -modules
Rosa Orellana, Mike Zabrocki
We consider the symmetric group -module of the polynomial ring with sets of commuting variables and sets of anti-commuting variables and show that the multipl…
An insertion algorithm on multiset partitions with applications to diagram algebras
Laura Colmenarejo, Rosa Orellana, Franco Saliola +2
We generalize the Robinson-Schensted-Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to new enumerative results that have representation…
A module for the Delta conjecture
Mike Zabrocki
We define a module that is an extension of the diagonal harmonics and whose graded Frobenius characteristic is conjectured to be the symmetric function expression which appears in…
The Hopf structure of symmetric group characters as symmetric functions
Rosa Orellana, Mike Zabrocki
In arXiv:1605.06672 the authors introduced inhomogeneous bases of the ring of symmetric functions. The elements in these bases have the property that they evaluate to characters of…
Products of characters of the symmetric group
Rosa Orellana, Mike Zabrocki
In a recent paper, the authors introduced a new basis of the ring of symmetric functions which evaluate to the irreducible characters of the symmetric group at roots of unity. The…
A proof of the -variable Catalan polynomial of the Delta conjecture
Mike Zabrocki
In The Delta Conjecture (arxiv:1509.07058), Haglund, Remmel and Wilson introduced a four variable Catalan polynomial, so named because the specialization of this polynomi…
Symmetric group characters as symmetric functions (extended abstract)
Rosa Orellana, Mike Zabrocki
The irreducible characters of the symmetric group are a symmetric polynomial in the eigenvalues of a permutation matrix. They can therefore be realized as a symmetric function that…
Some new applications of the Stanley-Macdonald Pieri Rules
A. M. Garsia, J. Haglund, G. Xin +1
In a seminal paper Richard Stanley derived Pieri rules for the Jack symmetric function basis. These rules were extended by Macdonald to his now famous symmetric function basis. The…
The Pieri rule for dual immaculate quasi-symmetric functions
Nantel Bergeron, Juana Sánchez-Ortega, Mike Zabrocki
The immaculate basis of the non-commutative symmetric functions was recently introduced by the first and third author to lift certain structures in the symmetric functions to the d…
Multiplicative structures of the immaculate basis of non-commutative symmetric functions
Chris Berg, Nantel Bergeron, Franco Saliola +2
We continue our development of a new basis for the algebra of non-commutative symmetric functions. This basis is analogous to the Schur basis for the algebra of symmetric functions…
Indecomposable modules for the dual immaculate basis of quasi-symmetric functions
Chris Berg, Nantel Bergeron, Franco Saliola +2
We construct indecomposable modules for the 0-Hecke algebra whose characteristics are the dual immaculate basis of the quasi-symmetric functions.
The immaculate basis of the non-commutative symmetric functions
Chris Berg, Nantel Bergeron, Franco Saliola +2
FPSAC 2013 Extended Abstract. We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build…
-Schur functions and affine Schubert calculus
Thomas Lam, Luc Lapointe, Jennifer Morse +3
This book is an exposition of the current state of research of affine Schubert calculus and -Schur functions. This text is based on a series of lectures given at a workshop titl…