✦ LIBER ✦
Almost all trees share a complete set of immanantal polynomials
✍ Scribed by Phillip Botti; Russell Merris
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 371 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Let χ be an irreducible character of the symmetric group S~n~. For an n‐by‐n matrix A = (a~ij~), define
equation image
If G is a graph, let D(G) be the diagonal matrix of its vertex degrees and A(G) its adjacency matrix. Let y and z be independent indeterminates, and define L(G) = yD(G) + zA(G). Suppose t~n~ is the number of trees on n vertices and s~n~ is the number of such trees T for which there exists a nonisomorphic tree T̃ such that d~χ~(xl ‐ L(T)) = d~x~(xl ‐ L(T̃)) for every irreducible character χ of S~n~. Then lim~n→∞~ S~n~/t~n~ = 1. © 1993 John Wiley & Sons, Inc.