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Generalizations of Rook Polynomials

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Author(s): Morris Dworkin
Series: PhD thesis at Brandeis University
Year: 1997

Language: English

Title
Abstract
Contents
Part I: The Cover Polynomial
1. Introduction to Part I
2. Definitions
3. Factorization of the Cover Polynomial of Ferrers Boards
4. Partial Factorization of the Cover Polynomial of Skyline Boards
5. Proof of the Partial Factorization Theorem
6. Applications of the Partial Factorization Theorem
7. Partial Factorization of Column-Permuted Staircase Boards
Part II: q-Analogues
8. Introduction to Part II
9. Permutations With Restricted Position
10. Introduction to q-Analogues
11. Two q-Analogues of the Derivation of the Factorial Rook Polynomial
12. Garsia and Remmel’s q-Analogue
13. A New Recurrence for Garsia and Remmel’s q-Hit Numbers
14. A Combinatorial Interpretation for the Ntilde_i
15. A Reciprocity Theorem
16. Symmetry Within the q-Hit Numbers
17. Other Questions
Appendix: Column-Permuted Staircase Boards
References