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)
On a matroid identity
β Scribed by James G. Oxley
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 443 KB
- Volume
- 44
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
The purpose of this note is to prove an identity for generalized Tuttffirothendieck invariants. at least two special cases of which have already proved to be of considerable use. In addition, one of these special cases is used to strengthen results of Lindstriim on the critical exponent of a representable matroid and the chromatic number of a regular matroid.
π SIMILAR VOLUMES
## dedicated to professor w. t. tutte on the occasion of his eightieth birthday We present several new polynomial identities associated with matroids and geometric lattices and relate them to formulas for the characteristic polynomial and the Tutte polynomial. The identities imply a formula for th
If M is a loopless matroid in which MIX and MI Y are connected and X c~ Y is non-empty, then one easily shows that MI(X u Y) is connected. Likewise, it is straightforward to show that if G and H are n-connected graphs having at least n common vertices, then G u H is nconnected. The purpose of this n
We show that the set of r-quasi-transversals of a matroid, if nonempty, is the set of bases of a matroid. We also give an alternative proof of the known theorem which identifies the conjugate of the rank partition of a matroid.