Abstract
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 n × 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.
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© 1999 Kluwer Academic Publishers
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Haglund, J., Ono, K., Wagner, D.G. (1999). Theorems and Conjectures Involving Rook Polynomials with Only Real Zeros. In: Ahlgren, S.D., Andrews, G.E., Ono, K. (eds) Topics in Number Theory. Mathematics and Its Applications, vol 467. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0305-3_13
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DOI: https://doi.org/10.1007/978-1-4613-0305-3_13
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