Pfaffian and Hafnian identities in shuffle algebras

DOI10.1016/S0196-8858(02)00036-2zbMath1018.05006arXivmath/0204026MaRDI QIDQ1867018

Jean-Yves Thibon, Jean-Gabriel Luque

Publication date: 2 April 2003

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0204026

zbMATH Keywords

combinatorial identitiessymmetric functionsmultiple integralsshuffle algebrasWick formulaPfaffian identitiesde Bruijn formulaHafnian identitiesshuffle identities

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Symmetric functions and generalizations (05E05) Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Associative rings and algebras with additional structure (16W99)

Related Items (17)

The partition function of log-gases with multiple odd charges ⋮ The Grassmann-Berezin calculus and theorems of the matrix-tree type ⋮ Replacing Pfaffians and applications ⋮ Quantum permanents and Hafnians via Pfaffians ⋮ A sign-reversing involution for an extension of Torelli's Pfaffian identity ⋮ Quantum hyperdeterminants and hyper-Pfaffians ⋮ Quantum Pfaffians and hyper-Pfaffians ⋮ Generating functions and counting formulas for spanning trees and forests in hypergraphs ⋮ Ensemble averages when \(\beta \) is a square integer ⋮ Generalizations of Cauchy's determinant and Schur's Pfaffian ⋮ A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn's formula ⋮ Hyperdeterminantal expressions for Jack functions of rectangular shapes ⋮ Exit problems associated with finite reflection groups ⋮ Pfaffians and representations of the symmetric group ⋮ Invariants of multidimensional time series based on their iterated-integral signature ⋮ Asymptotics of Selberg-like integrals: The unitary case and Newton's interpolation formula ⋮ Applications of minor summation formula. III: Plücker relations, lattice paths and Pfaffian identities

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