Further Investigations Involving Rook Polynomials With Only Real Zeros
نویسندگان
چکیده
منابع مشابه
Further Investigations Involving Rook Polynomials With Only Real Zeros
We study the zeros of two families of polynomials related to rook theory and matchings in graphs. One of these families is based on the cover polynomial of a digraph introduced by Chung and Graham [ChGr]. Another involves a version of the \hit polynomial" of rook theory, but which applies to weighted matchings in (non-bipartite) graphs. For both of these families we prove a result which is anal...
متن کاملFurther Investigations Involving Rook Polynomials with Only Real Roots
We present a number of conjectures involving rook polynomials having only real zeros. Many of these generalize a previous conjecture of the author, K. Ono, and D. G. Wagner, namely that if A is a real n n matrix which is weakly increasing down columns, then the permanent of zA + Jn has only real zeros. In some cases these conjectures are motivated by factorization theorems for Ferrers boards. S...
متن کاملTheorems and Conjectures Involving Rook Polynomials with Only Real Zeros
Let A = (aij) be a real n n matrix with non-negative entries which are weakly increasing down columns. If B = (bij) is the n n matrix where bij := aij+z; then we conjecture that all of the roots of the permanent of B, as a polynomial in z; are real. Here we establish several special cases of the conjecture.
متن کاملPolynomials with only real zeros 1
Conditions which ensure that a combination of real polynomials, which have real interlacing zeros, continues to have only real zeros are derived. This gives a generalization of a result of Haglund and is proved using a unified method of Liu-Wang-Yeh.
متن کاملTheorems and Conjectures Involving Rook Polynomials with Real Roots
Let A = (a ij) be a real n n matrix with non-negative entries which are weakly increasing down columns. If B = (b ij) is the nn matrix where b ij := a ij +z; then we conjecture that all of the roots of the permanent of B, as a polynomial in z; are real. Here we establish several special cases of the conjecture.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2000
ISSN: 0195-6698
DOI: 10.1006/eujc.2000.0422