A sign-reversing involution for an extension of Torelli's Pfaffian identity

Richard Ehrenborg, N. Bradley Fox

Research output: Contribution to journalArticlepeer-review


We evaluate the hyperpfaffian of a skew-symmetric k-ary polynomial f of degree k/2·(n-1). The result is a product of the Vandermonde product and a certain expression involving the coefficients of the polynomial f. The proof utilizes a sign reversing involution on a set of weighted, oriented partitions. When restricting to the classical case when k=2 and the polynomial is (xj -xi)n-1, we obtain an identity due to Torelli.

Original languageEnglish
Pages (from-to)69-74
Number of pages6
JournalDiscrete Mathematics
StatePublished - Oct 6 2014

Bibliographical note

Funding Information:
The authors are grateful to the referees for their comments on an earlier version of this note. The first author was partially supported by National Science Foundation grant DMS 0902063 .


  • Exterior algebra
  • Hyperpfaffian
  • Pfaffian
  • Sign-reversing involution
  • The Vandermonde identity
  • Torelli's identity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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