A new approach to word standardization and some of its applications
Turkish Journal of Mathematics, cilt.46, sa.Special Issue 2, ss.2003-2014, 2022 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 46 Sayı: Special Issue 2
- Basım Tarihi: 2022
- Doi Numarası: 10.55730/1300-0098.3248
- Dergi Adı: Turkish Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.2003-2014
- Anahtar Kelimeler: RSK the correspondence of Robinson-Schensted-Knuth, Young tableaux, word standardization, Knuth equivalent of words, Eulerian number
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Ankara Yıldırım Beyazıt Üniversitesi Adresli: Evet
Özet
© 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)