A new approach to word standardization and some of its applications

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Turkish Journal of Mathematics, vol.46, no.Special Issue 2, pp.2003-2014, 2022 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: Special Issue 2
  • Publication Date: 2022
  • Doi Number: 10.55730/1300-0098.3248
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2003-2014
  • Keywords: Eulerian number, Knuth equivalent of words, Rsk the correspondence of robinson–schensted–knuth, Word standardization, Young tableaux


© TÜBİTAKIn this article, we study word standardization in comparison to Young tableau standardization. We count the number of words (respectively Young tableau) standardized to a given permutation (respectively to a given standard Young tableau). We prove that both rectification and standardization applications commute and show that the standardization commutes with the insertion of Robinson–Schensted. We show that the standardizations of Knuth-equivalent two words are also Knuth equivalent. Finally, using word standardization we establish a proof for the following well-known equality (Formula Presented)