Luis Serrano

Luis Serrano
Université du Québec à Montréal | UQAM · Department of Mathematics

PhD

About

19
Publications
610
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
265
Citations
Additional affiliations
July 2010 - August 2014

Publications

Publications (19)
Article
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...
Article
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...
Article
We construct indecomposable modules for the 0-Hecke algebra whose characteristics are the dual immaculate basis of the quasi-symmetric functions.
Article
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.
Article
Full-text available
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...
Article
Full-text available
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.
Article
Full-text available
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.
Article
Full-text available
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.
Article
Full-text available
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...
Article
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...
Article
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...
Article
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...
Article
Full-text available
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...
Article
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...
Article
Full-text available
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...
Article
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...
Article
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...
Article
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...
Article
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...

Network

Cited By