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Abstract: 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 \Theta 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. Special cases are shown to follow from a theorem of Szego. We also present a weighted version... (Update)
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.... 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 ij ) is defined by per A = X w2Sn a 1;w(1) a...
.... simply state the most central of these problems, which is due to Haglund, Ono, and Wagner [47] For further problems of this nature, see [46]. Recall from the previous section that the permanent of an n n matrix A = a ij ) is de ned by per A = a 1;w(1) a 2;w(2) a...
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BibTeX entry: (Update)
J. Haglund, Further investigations involving rook polynomials with only real roots, preprint dated April 9, 1998. http://citeseer.ist.psu.edu/haglund98further.html More
@misc{ haglund98further,
author = "J. Haglund",
title = "Further investigations involving rook polynomials with only real roots",
text = "J. Haglund, Further investigations involving rook polynomials with only
real roots, preprint dated April 9, 1998.",
year = "1998",
url = "citeseer.ist.psu.edu/haglund98further.html" }
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8 The problem of the rooks and its applications (context) - Kaplansky, Riordan - 1946
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6 private communication (context) - Reiner, White
6 and Permutations of Vectors (context) - Haglund, Rook - 1993
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3 Bemerkungen zu einem Satz von J (context) - Szego - 1922
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3 and zeta functions (context) - Haglund, theory - 1996
3 Gauther-Villars (context) - Laguerre, vol
2 On generating functions of totally positive matrices (context) - Schoenberg - 1952
2 On permanents and the zeros of the rook polynomials (context) - Niejenhuis - 1976
2 Colored juggling patterns and weighted rook placements (context) - Ehrenborg, Haglund et al.
2 Zwei Satze uber algebraische gleidhungen mit laiter reellen .. (context) - Schur - 1914
2 log-concave and P'olya frequency series in combinatorics (context) - Brenti - 1989
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