𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The Determinant Formula for a Matroid Bilinear Form

✍ Scribed by T. Brylawski; A. Varchenko

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
416 KB
Volume
129
Category
Article
ISSN
0001-8708

No coin nor oath required. For personal study only.

✦ Synopsis

We introduce a symmetric bilinear form of a weighted matroid and prove that the determinant of the matrix of this form is a product of linear functions of weights. This formula is an analog of the formula for the determinant of the Shapovalov form in representation theory.

πŸ“œ SIMILAR VOLUMES

A MΓΆbius Identity Arising from Modularit
A MΓΆbius Identity Arising from Modularity in a Matroid Bilinear Form
✍ T. Brylawski πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 176 KB

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)

A simple closed-form formula for the mut
A simple closed-form formula for the mutual impedance of dipoles
✍ A. Kazemipour; X. Begaud πŸ“‚ Article πŸ“… 2002 πŸ› John Wiley and Sons 🌐 English βš– 114 KB

## Abstract A simple and compact formula of dipole mutual impedance is presented. This method gives an analytical expression of mutual impedance between two real, thick center‐fed dipoles in a general geometrical configuration for small distances. The results of this new formulation show a good agr