Mathematics – Combinatorics
Scientific paper
2002-04-02
Mathematics
Combinatorics
28 pages, LaTex. Minor typos corrected, two references added
Scientific paper
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 hyperpfaffians and hyperhafnians.
Luque Jean-Gabriel
Thibon Jean-Yves
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