๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Note on the Pfaffian Matrix-Tree Theorem

โœ Scribed by Scott Hirschman; Victor Reiner


Publisher
Springer Japan
Year
2004
Tongue
English
Weight
409 KB
Volume
20
Category
Article
ISSN
0911-0119

No coin nor oath required. For personal study only.


๐Ÿ“œ SIMILAR VOLUMES


Some determinant expansions and the matr
โœ J.W. Moon ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 513 KB

We derive an expansion for a certain determinant that involves two sets of formal variables. The result provides a unified approach to several known expansions including a generalized form of the matrix-tree theorem.

Note on the virial theorem
โœ Q. K. Ghori ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› The Chinese Society of Theoretical and Applied Mec ๐ŸŒ English โš– 102 KB
Multivariable Lagrange Inversion, Gessel
โœ I.P Goulden; D.M Kulkarni ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 315 KB

A new form of multivariable Lagrange inversion is given, with determinants occurring on both sides of the equality. These determinants are principal minors, for complementary subsets of row and column indices, of two determinants that arise singly in the best known forms of multivariable Lagrange in

Bideterminants, arborescences and extens
โœ M. Minoux ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 394 KB

The Matrix-Tree Theorem is a well-known combinatorial result relating the value of the minors of a certain square matrix to the sum of the weights of the arborescences (= rooted directed trees) in the associated graph. We prove an extension of this result to algebraic structures much more general th