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Abstract: Let A = (a ij ) be a real n \Theta n matrix with non-negative entries which are weakly increasing down columns. If B = (b ij ) is the n \Theta n 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. (Update)
Context of citations to this paper: More
...in the combinatorial subject of rook theory. We will simply state the most central of these problems, which is due to Haglund, Ono, and Wagner [43]. For further problems of this nature, see [42] Recall from the previous section that the permanent of an n Theta n matrix A = a...
...a n;oe(n) Let Jn denote the n Theta n matrix of all ones. Recently the author, K. Ono, and D. G. Wagner made the following conjecture [HOW]: Monotone Column Permanent (MCP) Conjecture. Let A be a real n Theta n matrix whose entries are weakly increasing down columns, i.e. a...
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BibTeX entry: (Update)
J. Haglund, K. Ono, and D. G. Wagner, Theorems and conjectures involving rook polynomials with real roots, in Proc. Topics in Number Theory and Combinatorics, State College, PA (1997), to appear. http://citeseer.ist.psu.edu/haglund97theorems.html More
@misc{ haglund97theorems,
author = "J. Haglund and K. Ono and D. Wagner",
title = "Theorems and conjectures involving rook polynomials with real roots",
text = "J. Haglund, K. Ono, and D. G. Wagner, Theorems and conjectures involving
rook polynomials with real roots, in Proc. Topics in Number Theory and Combinatorics,
State College, PA (1997), to appear.",
year = "1997",
url = "citeseer.ist.psu.edu/haglund97theorems.html" }
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