Journal of Integer Sequences, Vol. 14 (2011), Article 11.3.5

Square Involutions


Filippo Disanto
Dipartimento di Scienze Matematiche e Informatiche
Università di Siena
Pian dei Mantellini 44
53100 Siena, Italy

Andrea Frosini
Dipartimento di Sistemi e Informatica
Università degli Studi di Firenze
Viale Morgagni 65
50134 Firenze, Italy

Simone Rinaldi
Dipartimento di Scienze Matematiche e Informatiche
Università di Siena
Pian dei Mantellini 44
53100 Siena, Italy

Abstract:

A square involution is a square permutation which is also an involution. In this paper we give the enumeration of square involutions, using purely combinatorial methods, by establishing a bijective correspondence with a class of lattice paths. As a corollary to our result, we enumerate various subclasses of square involutions, including the classes of triangular, decomposable, and fat involutions.

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(Concerned with sequences A000079 A001405 A027306 A100071 A130783 A164990 A164991.)

Received November 16 2010; revised version received February 22 2011. Published in Journal of Integer Sequences, March 25 2011.

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