2004/07/01 by Abigail G. Mitchell, Mitchell, Abigail G. · 1 citation
Engineering · Mathematics · #05A05 #05A15 (Primary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO #msc:05A05 #msc:05A15
paper · pdf · doi:10.48550/arxiv.math/0407007
7 pages
arxiv created 2004/07/01 · openalex publication_date 2004/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Rook polynomials have been studied extensively since 1946, principally as a method for enumerating restricted permutations. However, they have also been shown to have many fruitful connections with other areas of mathematics, including graph theory, hypergeometric series, and algebraic geometry. It is known that the rook polynomial of any board can be computed recursively. The naturally arising inverse question -- given a polynomial, what board (if any) is associated with it? -- remains open. In this paper, we solve the inverse problem completely for the class of Ferrers boards, and show that the increasing Ferrers board constructed from a polynomial is unique.