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Title:
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A note on flips in diagonal rectangulations
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Author:
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Cardinal, Jean; Sacristán Adinolfi, Vera; Silveira, Rodrigo Ignacio
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. CGA -Computational Geometry and Applications |
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Abstract:
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Rectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. Other results deal with local changes involving a single edge of a rectangulation, referred to as flips, edge rotations, or edge pivoting. Such operations induce a graph on equivalence classes of rectangulations, related to so-called flip graphs on triangulations and other families of geometric partitions. In this note, we consider a family of flip operations on the equivalence classes of diagonal rectangulations, and their interpretation as transpositions in the associated Baxter permutations, avoiding the vincular patterns { 3{14}2, 2{41}3 }. This complements results from Law and Reading (JCTA, 2012) and provides a complete characterization of flip operations on diagonal rectangulations, in both geometric and combinatorial terms. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
-Computer science--Mathematics
-Numerical analysis
-rectangulations
-flip graphs
-pattern-avoiding permutations
-Informàtica--Matemàtica
-Anàlisi numèrica
-Classificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science
-Classificació AMS::65 Numerical analysis::65D Numerical approximation and computational geometry |
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Rights:
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Document type:
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Article - Submitted version
Article |
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Published by:
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Chapman & Hall/CRC
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