From Dyck Paths to Standard Young Tableaux

Juan B. Gil, Peter R.W. McNamara, Jordan O. Tirrell, Michael D. Weiner

Research output: Contribution to journalArticlepeer-review


We present nine bijections between classes of Dyck paths and classes of standard Young tableaux (SYT). In particular, we consider SYT of flag and rectangular shapes, we give Dyck path descriptions for certain SYT of height at most 3, and we introduce a special class of labeled Dyck paths of semilength n that is shown to be in bijection with the set of all SYT with n boxes. In addition, we present bijections from certain classes of Motzkin paths to SYT. As a natural framework for some of our bijections, we introduce a class of set partitions which in some sense is dual to the known class of noncrossing partitions.

Original languageEnglish (US)
Pages (from-to)69-93
Number of pages25
JournalAnnals of Combinatorics
Issue number1
StatePublished - Mar 1 2020

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics


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