Rayleigh monotonicity in Physics has a combinatorial interpretation. In this paper we give a combinatorial proof of the Rayleigh formula using the Jacobi Identity and the all-minors matrix tree Theorem. Motivated by the fact that the edge set of each spanning tree of G is a basis of the graphic matroid induced by G , we define the Rayleigh monotonicity of the generating polynomial for the set of bases of a matroid and suggest a few related problems.
%0 Journal Article
%1 choe08
%A Choe, YoungBin
%D 2008
%J Discrete Mathematics
%K combinatorics graph.theory matroid monotonicity rayleigh
%N 24
%P 5944--5953
%R 10.1016/j.disc.2007.11.011
%T A Combinatorial Proof of the Rayleigh Formula for Graphs
%V 308
%X Rayleigh monotonicity in Physics has a combinatorial interpretation. In this paper we give a combinatorial proof of the Rayleigh formula using the Jacobi Identity and the all-minors matrix tree Theorem. Motivated by the fact that the edge set of each spanning tree of G is a basis of the graphic matroid induced by G , we define the Rayleigh monotonicity of the generating polynomial for the set of bases of a matroid and suggest a few related problems.
@article{choe08,
abstract = {Rayleigh monotonicity in Physics has a combinatorial interpretation. In this paper we give a combinatorial proof of the Rayleigh formula using the Jacobi Identity and the all-minors matrix tree Theorem. Motivated by the fact that the edge set of each spanning tree of G is a basis of the graphic matroid induced by G , we define the Rayleigh monotonicity of the generating polynomial for the set of bases of a matroid and suggest a few related problems. },
added-at = {2016-06-07T11:32:54.000+0200},
author = {Choe, YoungBin},
biburl = {https://www.bibsonomy.org/bibtex/2d5e63b667bd502ef686d4545cac03e33/ytyoun},
doi = {10.1016/j.disc.2007.11.011},
interhash = {4b5dcacc1dfd2c3123f7d7caaf700906},
intrahash = {d5e63b667bd502ef686d4545cac03e33},
issn = {0012-365X},
journal = {Discrete Mathematics },
keywords = {combinatorics graph.theory matroid monotonicity rayleigh},
number = 24,
pages = {5944--5953},
timestamp = {2016-06-07T11:37:53.000+0200},
title = {A Combinatorial Proof of the {Rayleigh} Formula for Graphs },
volume = 308,
year = 2008
}