A Bijection for Crossings and Nestings

2012/09/14 by Lily Yen, Yen, Lily
Computer Science · Mathematics · #05A19 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Data Management and Algorithms #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1209.3082

openalex publication_date 2012/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a subclass of matchings, set partitions, and permutations, we describe a direct bijection involving only arc annotated diagrams that not only interchanges maximum nesting and crossing numbers, but also all refinements of crossing and nesting numbers. Furthermore, we show that the bijection cannot be applied to a similar class of coloured arc annotated diagrams.

Citations

• Crossings and alignments of permutations

Related

• Crossings and nestings in set partitions of classical types
• Crossings and Nestings of Matchings and Partitions
• Pattern avoidance in matchings and partitions
• Noncrossing arc diagrams and canonical join representations
• Crossing and alignments of permutations