Pfaffian and Hafnian identities in shuffle algebras
Authors: Luque, J-G.; Thibon, J-Y.
Source: Advances in Applied Mathematics, Volume 29, Number 4, November 2002 , pp. 620-646(27)
Publisher: Academic Press
Chen's lemma on iterated integrals implies that certain identities involving multiple integrals, such as the de Bruijn and Wick formulas, amount to combinatorial identities for Pfaffians and Hafnians in shuffle algebras. We provide direct algebraic proofs of such shuffle identities, and obtain various generalizations. We also discuss some Pfaffian identities due to Sundquist and Ishikawa–Wakayama, and a Cauchy formula for anticommutative symmetric functions. Finally, we extend some of the previous considerations to hyper-Pfaffians and hyper-Hafnians.
© 2002 Elsevier Science (USA)
Document Type: Research Article
Publication date: November 1, 2002