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

Richard Ehrenborg; N. Bradley Fox

doi:10.1016/j.disc.2014.06.002

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

Richard Ehrenborg
, N. Bradley Fox

Mathematics

Producción científica: Article › revisión exhaustiva

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	69-74
Número de páginas	6
Publicación	Discrete Mathematics
Volumen	332
DOI	https://doi.org/10.1016/j.disc.2014.06.002
Estado	Published - oct 6 2014

Nota bibliográfica

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 .

Financiación

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 .

Financiadores	Número del financiador
National Science Foundation Arctic Social Science Program	DMS 0902063
Directorate for Mathematical and Physical Sciences	0902063

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2014.06.002

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title = "A sign-reversing involution for an extension of Torelli's Pfaffian identity",

abstract = "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.",

keywords = "Exterior algebra, Hyperpfaffian, Pfaffian, Sign-reversing involution, The Vandermonde identity, Torelli's identity",

author = "Richard Ehrenborg and Fox, \{N. Bradley\}",

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 . ",

year = "2014",

month = oct,

day = "6",

doi = "10.1016/j.disc.2014.06.002",

language = "English",

volume = "332",

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TY - JOUR

T1 - A sign-reversing involution for an extension of Torelli's Pfaffian identity

AU - Ehrenborg, Richard

AU - Fox, N. Bradley

N1 - 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 .

PY - 2014/10/6

Y1 - 2014/10/6

N2 - 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.

AB - 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.

KW - Exterior algebra

KW - Hyperpfaffian

KW - Pfaffian

KW - Sign-reversing involution

KW - The Vandermonde identity

KW - Torelli's identity

UR - https://www.scopus.com/pages/publications/84903178091

UR - https://www.scopus.com/pages/publications/84903178091#tab=citedBy

U2 - 10.1016/j.disc.2014.06.002

DO - 10.1016/j.disc.2014.06.002

M3 - Article

AN - SCOPUS:84903178091

SN - 0012-365X

VL - 332

SP - 69

EP - 74

JO - Discrete Mathematics

JF - Discrete Mathematics

ER -

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

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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