Permutominoes are polyominoes defined by suitable pairs of permutations. In this paper we provide a formula to count the number of convex permutominoes of given perimeter. To this aim we define the transform of a generic pair of permutations, we characterize the transform of any pair defining a convex permutomino, and we solve the counting problem in the transformed space.
The Number of Convex Permutominoes / P. Boldi, V. Lonati, M. Santini, R. Radicioni - In: Pre-proccedings of the 1st International conference on language and automata theory and applications : LATA 2007 : March 29-April 4, 2007 / [a cura di] Universitat Rovira i Virgili : Research Graoup on Mathematical Linguistics. - Terragona : Universitat Rovira i Virgili, 2007. - pp. 151-162 (( Intervento presentato al 1. convegno International Conference on Language and Automata Theory and Applications tenutosi a Tarragona, Spain nel 2007.
The Number of Convex Permutominoes
P. BoldiPrimo
;V. LonatiSecondo
;M. SantiniPenultimo
;R. RadicioniUltimo
2007
Abstract
Permutominoes are polyominoes defined by suitable pairs of permutations. In this paper we provide a formula to count the number of convex permutominoes of given perimeter. To this aim we define the transform of a generic pair of permutations, we characterize the transform of any pair defining a convex permutomino, and we solve the counting problem in the transformed space.
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