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

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

2010-11-08

arxiv.org/abs/1011.1889v3

Mathematics

Combinatorics

Scientific paper

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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