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Factorization of the Cover Polynomial

✍ Scribed by Morris Dworkin

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 496 KB
Volume: 71
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1997.1745

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✦ Synopsis

Chung and Graham's cover polynomial is a generalization of the factorial rook polynomial in which the second variable keeps track of cycles. We factor the cover polynomial completely for Ferrers boards with either increasing or decreasing column heights. For column-permuted Ferrers boards, we find a sufficient condition for partial factorization. We apply this result to several special cases, including column-permuted ``staircase boards,'' getting a partial factorization in terms of the column permutation, as well as a sufficient condition for complete factorization. We conclude with some conjectures.

1997 Academic Press

We investigate the factorization of the cover polynomial for Ferrers boards, and, more generally, for column-permuted Ferrers boards, or ``skyline'' boards.

For Ferrers boards with increasing column heights the cover polynomial is a product of linear factors; this result, discovered independently by article no. TB971745 17 0095-8956Â97 25.00

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