Rook polynomials

• Main Authors: Tsai Chih-Jung, 蔡志榮
• Other Authors: Chin-Mei Kau Fu
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/05609068805478529612

碩士 === 淡江大學 === 中等學校教師在職進修數學教學碩士學位班 === 100 === In combinatorial mathematics, a rook polynomial is a generating function of the number of ways to place non-attacking rooks on a board that looks like a checker board; that is, no two rooks can be placed in the same row or same column. The term "rook polynomial" was coined by John Riordan. Despite the name''s derivation from chess, the impetus for studying rook polynomials is their connection with counting the number of permutations with restricted positions. In this thesis, we mainly obtain the rook polynomials of four special boards: 1.The rook polynomial of m×n chess board. 2.The rook polynomial with restricted area 3.The rook polynomial of path chess board 4.The rook polynomial of cycle chess board