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(b) Find the rook polynomial for the darkened squares in part (a).

(b) Find the rook polynomial for the darkened squares in part (a).

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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please answer part b

11, An ascent in a permutation is a consecutive pair of the form i, i + 1. The ascents in the following permutation are underlined: 12534. (a) Design a chessboard to represent a permutation of 1, 2, 3, 4, 5 so that a check in entry (i, j) means i is followed immediately by j in the permutation. Darken entries so as to exclude all ascents. (b) Find the rook polynomial for the darkened squares in part (a). (c) Find the number of permutations of 1, 2, 3, 4, 5 with k ascents. (Hint: See Theorem 2 in Section 8.2.)
Transcribed Image Text:11, An ascent in a permutation is a consecutive pair of the form i, i + 1. The ascents in the following permutation are underlined: 12534. (a) Design a chessboard to represent a permutation of 1, 2, 3, 4, 5 so that a check in entry (i, j) means i is followed immediately by j in the permutation. Darken entries so as to exclude all ascents. (b) Find the rook polynomial for the darkened squares in part (a). (c) Find the number of permutations of 1, 2, 3, 4, 5 with k ascents. (Hint: See Theorem 2 in Section 8.2.)
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