Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3248
Abstract
In 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: $$ \forall l \in \left\lbrace 0,1,\ldots,n-1\right\rbrace ,~~\left \langle {n\atop l} \right \rangle=d_{n,l}=a_{n,l}= \sum_{0\leq k \leq l}(-1)^k { n+1 \choose k } (l+1-k)^n. $$
Keywords
RSK the correspondence of Robinson-Schensted-Knuth, Young tableaux, word standardization, Knuth equivalent of words, Eulerian number
First Page
2003
Last Page
2014
Recommended Citation
TALAB, WESAM
(2022)
"A new approach to word standardization and some of its applications,"
Turkish Journal of Mathematics: Vol. 46:
No.
5, Article 27.
https://doi.org/10.55730/1300-0098.3248
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss5/27
