A Möbius Identity Arising from Modularity in a Matroid Bilinear Form

✍ Scribed by T. Brylawski

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 176 KB
• Volume: 91
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.2000.3109

✦ Synopsis

The matrix for the bilinear form of the flag space of a matroid has (with respect to an appropriate basis) a tensor product structure when the matroid has a modular flat K. When determinants are taken, an identity is obtained for the rho function (a certain product of the Mo bius and beta functions) summed over flats with a fixed intersection with K. When the identity is interpreted for Dowling lattices and finite projective spaces, identities with similar combinatorial proofs are obtained for binomial and Gaussian coefficients, respectively.

2000 Academic Press E poi che la sua mano a la mia puose Con lieto volto, ond'io mi confortai, Mi mise dentro a le segrete cose. ``Inferno,'' canto III, 7