Pieri and Cauchy Formulae for Ribbon Tableaux (2008)
Séries Formelles, Combinatoire Algébrique, Thomas Lam
Abstract. In [LLT] Lascoux, Leclerc and Thibon introduced symmetric functions Gλ which are spin and weight generating functions for ribbon tableaux. This article is aimed at studying these
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Anne Schilling
Virtual crystal structure on rigged configurations
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Sergi Elizalde, Kevin Woods
Bounds on the number of inference functions of a graphical model
Some Expansions of the Dual Basis of Zλ (2008)
Séries Formelles, Combinatoire Algébrique, Amanda Riehl
A zigzag or ribbon is a connected skew diagram that contains no 2 × 2 boxes. Given a composition β = (β1,... βk), we let Zβ denote the skew Schur function corresponding to the zigzag shape whose...
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Federico Ardila, Sara Billey
Flag arrangements and triangulations of products of simplices.
Alternating Sign Matrices With One −1 Under Vertical Reflection (2008)
Séries Formelles, Combinatoire Algébrique, Pierre Lalonde
Abstract. We define a bijection that transforms an alternating sign matrix A with one −1 into a pair (N, E) where N is a (so called) neutral alternating sign matrix (with one −1) and E is an...
Enumerating Bases of Self-Dual Matroids (2008)
Séries Formelles, Combinatoire Algébrique, Molly Maxwell
Abstract. We define involutively self-dual matroids and prove a relationship between the bases and selfdual bases of these matroids. We use this relationship to prove an enumeration formula for the...
A Rook Theory Model for the Generalized p, q-Stirling Numbers of the First and Second Kind (2008)
Séries Formelles, Combinatoire Algébrique, Karen Sue Briggs
Abstract. In (EJC 11 (2004), #R84), Remmel and Wachs presented two natural ways to define p, qanalogues of the generalized Stirling numbers of the first and second kind, S 1 (α, β, r) and S 2 (α,...
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique
On the complexity of computing Kostka numbers and Littlewood-Richardson coefficients
Enumerating Bases of Self-Dual Matroids (2008)
Séries Formelles, Combinatoire Algébrique, Molly Maxwell
Abstract. We define involutively self-dual matroids and prove a relationship between the bases and selfdual bases of these matroids. We use this relationship to prove an enumeration formula for the...
COMME EXIGENCE PARTIELLE DU DOCTORAT EN MATH ÉMATIQUES PAR (2008)
Une Approche, Holonome À La, Combinatoire Algébrique, Marni Julie Mishna
ii This thesis is dedicated to the memory of a wonderful woman, my mother, Vicki Munn. iv Acknowledgements I offer the following people and organizations heartfelt appreciation for their...
The combinatorics of frieze patterns and Markoff numbers (2008)
Séries Formelles, Combinatoire Algébrique, Abstract This Article, Andy Itsara, Ian Le, Gregg Musiker, ...
Dylan Thurston, and Rui Viana, presents a combinatorial model based on perfect matchings that explains the symmetries of the numerical arrays that Conway and Coxeter dubbed frieze patterns. This...
Hankel Determinants for Some Common Lattice Paths (2008)
Séries Formelles, Combinatoire Algébrique, Robert A. Sulanke, Guoce Xin
Abstract. For a single value of ℓ, let f(n, ℓ) denote the number of lattice paths that use the steps (1, 1), (1, −1), and (ℓ,0), that run from (0, 0) to (n, 0), and that never run below the...
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Enrica Duchi, Gilles Schaeffer
A combinatorial approach to jumping particles I: maximal flow regime
Pieri’s Formula for Generalized Schur Polynomials (2008)
Séries Formelles, Combinatoire Algébrique, Numata Yasuhide
Abstract. We define a generalization of Schur polynomials as a expansion coefficient of generalized Schur operators. We generalize the Pieri’s formula to the generalized Schur polynomials....
The Partition Function of Andrews and Stanley and Al-Salam-Chihara Polynomials (2008)
Séries Formelles, Combinatoire Algébrique, Masao Ishikawa, Jiang Zeng
Abstract. For any partition λ let ω(λ) denote the four parameter weight
Strong Descent Numbers and Turán Type Theorems (Extended Abstract) (2008)
Séries Formelles, Combinatoire Algébrique, Ron M. Adin, Yuval Roichman
Abstract. For a permutation π in the symmetric group Sn let the total degree be its valency in the Hasse diagram of the strong Bruhat order on Sn, and let the down degree be the number of...
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique
Clusters, Coxeter-sortable elements and noncrossing partitions Extended abstract. Please cite only the full version, available on the arXiv.
Area of Catalan Paths on a Checkerboard (2008)
Séries Formelles, Combinatoire Algébrique, Szu-en Cheng, Sen-peng Eu, Tung-shan Fu
Abstract. It is known that the area of all Catalan paths of length n is equal to 4n − `2n+1 ´ , which coincides n with the number of inversions of all 321-avoiding permutations of length n + 1. In...
Deformed Universal Characters for Classical and Affine Algebras and the (2008)
Séries Formelles, Combinatoire Algébrique, Mark Shimozono, Mike Zabrocki
Abstract. Creation operators are given for three distinguished bases of the type BCD universal character ring of Koike and Terada. Deformed versions of these operators create symmetric functions...
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Erik Ouchterlony
Pattern avoiding doubly alternating permutations
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Cristian Lenart, Er Postnikov
Affine Weyl groups in K-theory and representation theory
On Inversions in Standard Young Tableaux (2008)
Séries Formelles, Combinatoire Algébrique, Michael Shynar
Abstract. In this work, we present the inversion number of a standard Young tableau, and determine its distribution over certain sets of standard Young tableaux. Specifically, the work determines the...
Alternating Sign Matrices With One −1 Under Vertical Reflection (2008)
Séries Formelles, Combinatoire Algébrique, Pierre Lalonde
Abstract. We define a bijection that transforms an alternating sign matrix A with one −1 into a pair (N, E) where N is a (so called) neutral alternating sign matrix (with one −1) and E is an...
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique
Central Delannoy numbers, Legendre polynomials, and a balanced join operation preserving the Cohen-Macaulay property
Restricted Patience Sorting and Barred Pattern Avoidance (2008)
Séries Formelles, Combinatoire Algébrique, Er Burstein, Isaiah Lankham
Abstract. Patience Sorting is a combinatorial algorithm that can be viewed as an iterated, non-recursive form of the Schensted Insertion Algorithm. In recent work the authors have shown that Patience...
Counting Unrooted Loopless Planar Maps (2008)
Séries Formelles, Combinatoire Algébrique, Valery A. Liskovets, Timothy R. Walsh
Abstract. We present a formula for the number of n-edge unrooted loopless planar maps considered up to orientation-preserving isomorphism. The only sum contained in this formula is over the divisors...
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Francesco Brenti, Victor Reiner, Yuval Roichman
Alternating subgroups of Coxeter groups (Extended Abstract)
A Four-Parameter Partition Identity (2008)
Séries Formelles, Combinatoire Algébrique, Cilanne E. Boulet
Abstract. We present a new partition identity and give a combinatorial proof of our result. This generalizes a result of Andrews ’ in which he considers the generating function for partitions with...
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Christine Bessenrodt
On bar partitions and spin character zeros
Rook Numbers and the Normal Ordering Problem (2008)
Séries Formelles, Combinatoire Algébrique, Anna Varvak
Abstract. For an element w in the Weyl algebra generated by D and U with relation DU = UD + 1, the normally ordered form is w = ci,jU iDj. We demonstrate that the normal order coefficients ci,j of a...
Major Indices, Mahonian Identities (2008)
Séries Formelles, Combinatoire Algébrique, Robert Shwartz, Robert Shwartz
Abstract. A classical result of MacMahon shows that the length function and the major index are equidistributed over the symmetric group. A long standing open problem is to extend the notion of major...
Bruhat Order on the Involutions of Classical Weyl Groups (2008)
Séries Formelles, Combinatoire Algébrique, Federico Incitti
Abstract. It is known that a Coxeter group W, partially ordered by the Bruhat order, is a graded poset, with rank function given by the length, and that it is EL-shellable, hence Cohen-Macaulay, and...
Littlewood-Richardson coefficients (2008)
Séries Formelles, Combinatoire Algébrique
On the complexity of computing Kostka numbers and
of Kazhdan-Lusztig polynomials (2008)
Séries Formelles, Combinatoire Algébrique
New results on the combinatorial invariance
A Solution to the Tennis Ball Problem (2008)
Séries Formelles, Combinatoire Algébrique, Anna De Mier, Marc Noy
Abstract. We present a complete solution to the so-called tennis ball problem, which is equivalent to counting lattice paths in the plane that use North and East steps and lie between certain...
Tamari Lattices and Non-crossing Partitions in Types B and D (2008)
Séries Formelles, Combinatoire Algébrique, Hugh Thomas
Abstract. The usual, or type An, Tamari lattice is a partial order on T A n, the triangulations of an (n + 3)gon. We define a partial order on T B n, the set of centrally symmetric triangulations of...
Chromatic Polynomials and Representations of the Symmetric Group (2008)
Séries Formelles, Combinatoire Algébrique, Norman Biggs
The chromatic polynomial P (G; k) is the function which gives the number of ways of colouring a graph G when k colours are available. The fact that it is a polynomial function of k is essentially a...
Two New Criteria for Comparison in the Bruhat Order (2008)
Séries Formelles, Combinatoire Algébrique, Brian Drake, Sean Gerrish, Mark Sk
Abstract. We give two new criteria by which pairs of permutations may be compared in defining the Bruhat order (of type A). One criterion utilizes totally nonnegative polynomials and the other...
Séries Formelles, Combinatoire Algébrique, Nathan Reading
Abstract. For an arbitrary finite Coxeter group W, we define the family of Cambrian lattices for W as quotients of the weak order on W with respect to certain lattice congruences. We associate to...
(1.1) Generalised Schur P–Functions and Weyl’s Denominator Formula (2008)
Séries Formelles, Combinatoire Algébrique, A M Hamel, R C King
Abstract. We derive a general identity that relates generalised P–functions to the product of a Schur function and 1≤i<j≤n (xi + yj). This result generalises a number of well–known results...
The number of Z-convex polyominoes (2008)
Séries Formelles, Combinatoire Algébrique, Enrica Duchi, Simone Rinaldi, Gilles Schaeffer
Abstract. In this paper we consider a restricted class of polyominoes that we call Z-convex polyominoes. Z-convex polyominoes are polyominoes such that any two pairs of cells can be connected by a...
On the Number of Factorizations of a Full Cycle (2008)
Séries Formelles, Combinatoire Algébrique, John Irving
Abstract. We give a new expression for the number of factorizations of a full cycle into an ordered product of permutations of specified cycle types. This is done through purely algebraic means,...
Statistics on Signed Permutations Groups (Extended Abstract) (2008)
Séries Formelles, Combinatoire Algébrique, Michael Fire
Abstract. A classical result of MacMahon shows that the length function and the major index are equidistributed over the symmetric groups. Through the years this result was generalized in various...
Séries Formelles, Combinatoire Algébrique, Christopher J. Hillar
Abstract. Let k be a field of characteristic zero and let f ∈ k[x]. The m-th cyclic resultant of f is rm = Res(f, xm − 1). We characterize polynomials having the same set of nonzero cyclic...
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Brendon Rhoades, Mark Sk
Kazhdan-Lusztig immanants and products of matrix minors, II
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Maxime Rey
A new construction of the Loday-Ronco algebra
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Sangwook Kim
Shellable complexes and topology of diagonal arrangements
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Gilbert Labelle, Cédric Lamathe
A theory of general combinatorial differential operators
An Arctic Circle Theorem For Groves (2008)
Séries Formelles, Combinatoire Algébrique, T. Kyle Petersen, David Speyer
Abstract. In earlier work, Jockusch, Propp, and Shor proved a theorem describing the limiting shape of the boundary between the uniformly tiled corners of a random tiling of an Aztec diamond and the...
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Er Mednykh, Roman Nedela
Counting unrooted hypermaps on closed orientable surface
Braided differential calculus and quantum Schubert calculus (2008)
Séries Formelles, Combinatoire Algébrique, Anatol N. Kirillov, Toshiaki Maeno
Abstract. We provide a new realization of the quantum cohomology ring of a flag variety as a certain commutative subalgebra in the cross product of the Nichols-Woronowicz algebras associated to a...
Restricted Dumont permutations, Dyck paths, and noncrossing partitions (2008)
Séries Formelles, Combinatoire Algébrique, Er Burstein, Sergi Elizalde, Toufik Mansour
Abstract. We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is in turn a Dumont permutation of the second kind. We also consider some...
A Hopf Algebra of Parking Functions (2008)
Séries Formelles, Combinatoire Algébrique
Abstract. If the moments of a probability measure on are interpreted as a specialization of complete homogeneous symmetric functions, its free cumulants are, up to sign, the corresponding...
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Michael Schlosser
“Elliptic ” enumeration of nonintersecting lattice paths
Coincidences among skew Schur functions (2008)
Séries Formelles, Combinatoire Algébrique, Victor Reiner, Kristin M. Shaw, Stephanie Van Willigenburg
Abstract. We define an equivalence relation on skew diagrams such that two skew diagrams are equivalent if and only if they give rise to equal skew Schur functions. Then we derive some necessary and...
On a Class of Totally Nonnegative f-immanants (2008)
Séries Formelles, Combinatoire Algébrique, Brendon Rhoades, Mark Sk
Abstract. We define a family of totally nonnegative polynomials of the form f(σ)x1,σ(1) · · · xn,σ(n) and show that this family generalizes all known totally nonnegative polynomials of the form...
Formal Power Series and Algebraic Combinatorics (2008)
Séries Formelles, Combinatoire Algébrique, Petter Brändén, Toufik Mansour
Finite automata and pattern avoidance in words
A Bijection for Unicellular Partitioned Bicolored Maps (2008)
Séries Formelles, Combinatoire Algébrique, E. Vassilieva, G. Schaeffer
Abstract. In the present paper we construct a bijection that relates a set CN,p,q of unicellular partitioned bicolored maps to a set of couples (t, σ) of ordered bicolored trees and partial...
A Polynomiality Property for Littlewood-Richardson Coefficients (2008)
Séries Formelles, Combinatoire Algébrique, Etienne Rassart
Abstract. We present a polynomiality property of the Littlewood-Richardson coefficients cν λµ. The coefficients are shown to be given by polynomials in λ, µ and ν on the cones of the chamber...
Bounds for the Growth Rate of Meander Numbers (2004)
M. H. Albert, M. S. Paterson, Séries Formelles, Combinatoire Algébrique, M. H. Albert, M. S. Paterson
We provide improvements on the best currently known upper and lower bounds for the exponential growth rate of meanders. The method of proof for the upper bounds is to extend the Goulden-Jackson...
Combinatorial Aspects of Abstract Young Representations (2004)
Séries Formelles, Combinatoire Algébrique, Extended Abstract, Ron M. Adin, Francesco Brenti, Yuval Roichman
Abstract. The goal of this paper is to give a new unified axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras. Building upon fundamental works by Young and...
Equi-distribution over Descent Classes of the Hyperoctahedral Group (2004)
Séries Formelles, Combinatoire Algébrique, Extended Abstract, Ron M. Adin, Francesco Brenti, Yuval Roichman
Abstract. A classical result of MacMahon shows that the length function and the major index are equidistributed over the symmetric group. Foata and Schützenberger gave a remarkable refinement and...