Enrica Duchi ; Dominique Poulalhon - On square permutations

dmtcs:3565 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science - https://doi.org/10.46298/dmtcs.3565
On square permutationsArticle

Authors: Enrica Duchi 1; Dominique Poulalhon 1

  • 1 Laboratoire d'informatique Algorithmique : Fondements et Applications

Severini and Mansour introduced $\textit{square polygons}$, as graphical representations of $\textit{square permutations}$, that is, permutations such that all entries are records (left or right, minimum or maximum), and they obtained a nice formula for their number. In this paper we give a recursive construction for this class of permutations, that allows to simplify the derivation of their formula and to enumerate the subclass of square permutations with a simple record polygon. We also show that the generating function of these permutations with respect to the number of records of each type is algebraic, answering a question of Wilf in a particular case.


Volume: DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: square permutations,generating function,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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