A simple bijection for enhanced, classical, and 2-distant k-noncrossing partitions

Juan B. Gil, Jordan O. Tirrell

Research output: Contribution to journalArticle


In this note, we give a simple extension map from partitions of subsets of [n] to partitions of [n+1], which sends δ-distant k-crossings to (δ+1)-distant k-crossings (and similarly for nestings). This map provides a combinatorial proof of the fact that the numbers of enhanced, classical, and 2-distant k-noncrossing partitions are each related to the next via the binomial transform. Our work resolves a recent conjecture of Zhicong Lin and generalizes earlier reduction identities for partitions.

Original languageEnglish (US)
Article number111705
JournalDiscrete Mathematics
Publication statusAccepted/In press - Jan 1 2019


All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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