## About

19

Publications

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267

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Introduction

**Skills and Expertise**

Additional affiliations

July 2010 - August 2014

## Publications

Publications (19)

We introduce explicit combinatorial interpretations for the coefficients in some of the transition matrices relating to skew Hall-Littlewood polynomials P"@l"/"@m(t) and Hivert@?s quasisymmetric Hall-Littlewood polynomials G"@c(t). More specifically, we provide:1.the G-expansions of the Hall-Littlewood polynomials P"@l(t), the monomial quasisymmetr...

We continue our development of a new basis for the algebra of non-commutative symmetric functions. This basis is analogous to the basis of Schur functions for the algebra of symmetric functions, and it shares many of its wonderful properties. For instance, in this article we describe non-commutative versions of the Littlewood–Richardson rule and th...

We construct indecomposable modules for the 0-Hecke algebra whose
characteristics are the dual immaculate basis of the quasi-symmetric
functions.

We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions and decompose Schur functions according to a signed combinatorial formula.

We introduce a new basis of the non-commutative symmetric functions whose
commutative images are Schur functions. Dually, we build a basis of the
quasi-symmetric functions which expand positively in the fundamental
quasi-symmetric functions and decompose Schur functions. We then use the basis
to construct a non-commutative lift of the Hall-Littlewo...

We apply down operators in the affine nilCoxeter algebra to yield explicit
combinatorial expansions for certain families of non-commutative k-Schur
functions. This yields a combinatorial interpretation for a new family of
k-Littlewood-Richardson coefficients.

We introduce dual Hopf algebras which simultaneously combine the concepts of
the k-Schur function theory with the quasi-symmetric Schur function theory. We
construct dual basis of these Hopf algebras with remarkable properties.

We study a family of operators on the affine nilCoxeter algebra. We use these
operators to prove conjectures of Lam, Lapointe, Morse, and Shimozono regarding
strong Schur functions.

We introduce explicit combinatorial interpretations for the coefficients in
some of the transition matrices relating to skew Hall-Littlewood polynomials
P_lambda/mu(x;t) and Hivert's quasisymmetric Hall-Littlewood polynomials
G_gamma(x;t). More specifically, we provide: 1) the G-expansions of the
Hall-Littlewood polynomials P_lambda, the monomial q...

International audience
We prove that the Lam-Shimozono ``down operator'' on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra of the affine nilCoxeter algebra. We use this to verify a conjecture of Berg, Bergeron, Pon and Zabrocki describing the expansion of k-Schur functions of ``near rectangles'' in the affine nilC...

We prove that the Lam-Shimozono “down operator” on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra. We use this to verify a conjecture of C. Berg et al. [Electron. J. Comb. 19, No. 2, Research Paper P55, 20 p., electronic only (2012; Zbl 1253.05138)] describing the expansion of non-commutative k-Schur functions of...

International audience
We exhibit a canonical connection between maximal $(0,1)$-fillings of a moon polyomino avoiding north-east chains of a given length and reduced pipe dreams of a certain permutation. Following this approach we show that the simplicial complex of such maximal fillings is a vertex-decomposable and thus a shellable sphere. In par...

We prove Stanley's conjecture that, if delta_n is the staircase shape, then
the skew Schur functions s_{delta_n / mu} are non-negative sums of Schur
P-functions. We prove that the coefficients in this sum count certain fillings
of shifted shapes. In particular, for the skew Schur function s_{delta_n /
delta_{n-2}}, we discuss connections with Euler...

We exhibit a canonical connection between maximal (0,1)-fillings of a moon
polyomino avoiding north-east chains of a given length and reduced pipe dreams
of a certain permutation. Following this approach we show that the simplicial
complex of such maximal fillings is a vertex-decomposable, and thus shellable,
sphere. In particular, this implies a p...

We show that the set R(w_0) of reduced expressions for the longest element in the hyperoctahedral group exhibits the cyclic sieving phenomenon. More specifically, R(w_0) possesses a natural cyclic action given by moving the first letter of a word to the end, and we show that the orbit structure of this action is encoded by the generating function f...

We introduce a shifted analog of the plactic monoid of Lascoux and Sch\"utzenberger, the \emph{shifted plactic monoid}. It can be defined in two different ways: via the \emph{shifted Knuth relations}, or using Haiman's mixed insertion. Applications include: a new combinatorial derivation (and a new version of) the shifted Littlewood-Richardson Rule...

The problem of counting ramified covers of a Riemann surface up to homeomorphism was proposed by Hurwitz in the late 1800’s. This problem translates combinatorially into factoring a permutation of specified cycle type, with certain conditions on the cycle types of the factors, such as minimality and transitivity.
Goulden and Jackson have given a p...

We provide a direct geometric bijection for the number of lattice paths that never go below the line y = kx for a positive integer k. This solu- tion to the Generalized Ballot Problem is in the spirit of the re∞ection principle for the Ballot Problem (the case k = 1), but it uses rotation instead of re∞ection. It also gives bijective proofs of the...

Abstract The problem of counting ramified covers of a Riemann surface up to homeo- morphism was proposed by Hurwitz in the late 1800’s. This problem translates combinatorially into factoring a permutation with a specified cycle type, with certain conditions on the cycle types of the factors, such as minimality and transitivity. Goulden and Jackson...