Standard Young tableaux and colored Motzkin paths

Sen Peng Eu*, Tung Shan Fu, Justin T. Hou, Te Wei Hsu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


In this paper, we propose a notion of colored Motzkin paths and establish a bijection between the n-cell standard Young tableaux (SYT) of bounded height and the colored Motzkin paths of length n. This result not only gives a lattice path interpretation of the standard Young tableaux but also reveals an unexpected intrinsic relation between the set of SYTs with at most 2. d+. 1 rows and the set of SYTs with at most 2. d rows.

Original languageEnglish
Pages (from-to)1786-1803
Number of pages18
JournalJournal of Combinatorial Theory. Series A
Issue number7
Publication statusPublished - 2013 Sept
Externally publishedYes


  • Bijection
  • Colored Motzkin paths
  • Shuffles of parenthesis systems
  • Standard Young tableaux

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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