Properties of four partial orders on standard Young tableaux
Journal of Combinatorial Theory. Series A, cilt.113, sa.6, ss.1092-1119, 2006 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 113 Sayı: 6
- Basım Tarihi: 2006
- Doi Numarası: 10.1016/j.jcta.2005.09.008
- Dergi Adı: Journal of Combinatorial Theory. Series A
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1092-1119
- Anahtar Kelimeler: Möbius function and poset homotopy type, Partial orders, Robinson-Schensted algorithm (RSK), Skew standard tableaux, Standard Young tableaux
- Boğaziçi Üniversitesi Adresli: Hayır
Özet
Let SYTn be the set of all standard Young tableaux with n cells. After recalling the definitions of four partial orders, the weak, KL, geometric and chain orders on SYTn and some of their crucial properties, we prove three main results:•Intervals in any of these four orders essentially describe the product in a Hopf algebra of tableaux defined by Poirier and Reutenauer.•The map sending a tableau to its descent set induces a homotopy equivalence of the proper parts of all of these orders on tableaux with that of the Boolean algebra 2[n - 1]. In particular, the Möbius function of these orders on tableaux is (- 1)n - 3.•For two of the four orders, one can define a more general order on skew tableaux having fixed inner boundary, and similarly analyze their homotopy type and Möbius function. © 2005 Elsevier Inc. All rights reserved.