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.
|Number of pages||6|
|State||Published - Oct 6 2014|
Bibliographical noteFunding 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
- Sign-reversing involution
- The Vandermonde identity
- Torelli's identity
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics