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Pré-Publication, Document De Travail Année : 2010

Orders induced by segments in floorplan partitions and (2-14-3,3-41-2)-avoiding permutations

Résumé

Floorplan partitions are certain tilings of a rectangle by other rectangles. There are natural ways to order their elements (rectangles and segments). In particular, Ackerman, Barequet, and Pinter studied a pair of orders induced by neighborhood relations between rectangles of a floorplan partition, and obtained a natural bijection between these pairs and (2-41-3, 3-14-2)-avoiding permutations (also known as Baxter permutations). In the present paper, we study a pair of orders induced by neighborhood relations between segments of a floorplan partition. We obtain a natural bijection between these pairs and another family of permutations, namely (2-14-3,3-41-2)-avoiding permutations. We also enumerate these permutations, investigate relations between the two kinds of pairs of orders --- and correspondingly, between (2-14-3,3-41-2)-avoiding permutations and Baxter permutations --- and study the special case of ``guillotine'' partitions.
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Dates et versions

hal-00534068 , version 1 (08-11-2010)
hal-00534068 , version 2 (17-12-2010)
hal-00534068 , version 3 (11-07-2011)
hal-00534068 , version 4 (06-09-2012)

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Andrei Asinowski, Gill Barequet, Mireille Bousquet-Mélou, Toufik Mansour, Ron Pinter. Orders induced by segments in floorplan partitions and (2-14-3,3-41-2)-avoiding permutations. 2010. ⟨hal-00534068v1⟩
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