POLINÔMIOS DE TORRE E APLICAÇÕES COM IMPLEMENTAÇÕES NO SAGEMATH

Abstract

In this article, we adopt the “survey” style, in which we compile and concatenate the main results and applications concern rook polynomials. This combinatorics concept allows us to associate enumeration problems with the distribution of non-attacking rooks on a board. The motivation to study this theory comes from the possibility of aggregating several combinatorial problems with restrictions in a single technique. Moreover, the visual character that can be used when creating an image of the board and its easy computational implementation. In Section 4, we show the method’s robustness by deducing results for derangement, derangement with repeated elements, permutations with fixed points, ranks of permutations, and discordant permutations. The text is plenty of good examples, we emphasize the resolution of the problem of coincidences and the problem of encounters. We provide an online complement, made in PreTeXt, containing the implementation codes in SageMath and their interactive versions, which
can be used by students and teachers who want to enhance their work.

Keywords: Rook Polynomial; Permutations with Constraints; Enumerative Combinatorics;
Problem of Encounters; Algorithms in SageMath.