A permutomino of size n is a polyomino determined by particular pairs of permutations of size n. Here we determine the combinatorial properties and, in particular, the characterization for the pairs of permutations defining convex permutominoes. Using such a characterization, these permutations can be uniquely represented in terms of the so-called square permutations, introduced by Mansour and Severini. We provide a closed formula for the number of these permutations with size n.
Permutations Defining Convex Permutominoes / A. BERNINI; F. DISANTO; R. PINZANI; S. RINALDI. - In: JOURNAL OF INTEGER SEQUENCES. - ISSN 1530-7638. - ELETTRONICO. - 10:(2007), pp. 1-26.
Permutations Defining Convex Permutominoes
BERNINI, ANTONIO;PINZANI, RENZO;
2007
Abstract
A permutomino of size n is a polyomino determined by particular pairs of permutations of size n. Here we determine the combinatorial properties and, in particular, the characterization for the pairs of permutations defining convex permutominoes. Using such a characterization, these permutations can be uniquely represented in terms of the so-called square permutations, introduced by Mansour and Severini. We provide a closed formula for the number of these permutations with size n.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.