A bijective proof of Macdonald's reduced word formula

DOI10.5802/alco.23zbMath1409.05024arXiv1702.02936OpenAlexW2578780962WikidataQ114013413 ScholiaQ114013413MaRDI QIDQ1740605

Sara C. Billey, Alexander E. Holroyd, Benjamin J. Young

Publication date: 30 April 2019

Published in: Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.02936

zbMATH Keywords

shapespermutationsYoung tableauxSchubert polynomialsreduced wordsidentityenumeration of plane partitionsFerrers shapeMacdonald's formulaStanley's formula

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial aspects of partitions of integers (05A17) Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Grassmannians, Schubert varieties, flag manifolds (14M15) Markov processes (60J99)

Related Items

Inclusion-exclusion on Schubert polynomials, Principal specialization of dual characters of flagged Weyl modules, Bijective proofs of Monk's rule for Schubert and double Schubert polynomials with bumpless pipe dreams, Lenart's bijection via bumpless pipe dreams, The range of repetition in reduced decompositions, Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley, Bijective proofs of Monk's rule for Schubert and double Schubert polynomials with bumpless pipe dreams, Principal specializations of Schubert polynomials in classical types, Principal specializations of Schubert polynomials in classical types, Involution pipe dreams, Pipe dreams for Schubert polynomials of the classical groups, Hook formulas for skew shapes. III: Multivariate and product formulas

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A combinatorial approach to the \(q,t\)-symmetry relation in Macdonald polynomials
• Maximal fillings of Moon polyominoes, simplicial complexes, and Schubert polynomials
• Coxeter-Knuth graphs and a signed little map for type B reduced words
• Relating Edelman-Greene insertion to the Little map
• Statistics on wreath products, perfect matchings, and signed words
• Poset edge densities, nearly reduced words, and barely set-valued tableaux
• Gröbner geometry of Schubert polynomials
• Counting polygon dissections in the projective plane
• A bijective proof of a major index theorem of Garsia and Gessel
• Chains in the Bruhat order
• Flagged Schur functions, Schubert polynomials, and symmetrizing operators
• Schubert polynomials and the Littlewood-Richardson rule
• On the number of reduced decompositions of elements of Coxeter groups
• Odd symplectic groups
• Young-diagrammatic methods for the representation theory of the classical groups of type \(B_ n\), \(C_ n\), \(D_ n\)
• A new look at the permutations of the first n natural numbers
• Some combinatorial properties of Schubert polynomials
• Schubert polynomials and the nilCoxeter algebra
• Reduced words and plane partitions
• A weighted enumeration of maximal chains in the Bruhat order
• The Prism tableau model for Schubert polynomials
• A unified approach to combinatorial formulas for Schubert polynomials
• Factorization of the Robinson-Schensted-Knuth correspondence
• Transition formulas for involution Schubert polynomials
• Balanced tableaux
• Combinatorial aspects of the Lascoux-Schützenberger tree
• The Yang-Baxter equation, symmetric functions, and Schubert polynomials
• New symmetric plane partition identities from invariant theory work of De Concini and Procesi
• \(k\)-Schur functions and affine Schubert calculus
• The statistics of dimers on a lattice
• A Combinatorial Property of q-Eulerian Numbers
• RC-Graphs and Schubert Polynomials
• On the Netto Inversion Number of a Sequence
• An Eulerian partner for inversions