On the Tymoczko Codes for Standard Young Tableaux
Abstract
Given a partition $\lambda$ of integer $n>0$, there exists a diagram (called Young diagram $\mathcal{ Y}_{\lambda}$) associated with $\lambda$. The filling of such diagram from $[n]$ such that the entries increase from top to bottom and from left to right is called the standard Young tableaux ($ SYT$) of shape $\lambda$. In this paper, we associate an invariant with each standard Young tableau of shape $\lambda$, and provide some combinatorial interpretations of these invariants.
References
Assaf, S., & Schilling, A. (2018). A demazure crystal construction for Schubert polynomials. Algebraic Combinatorics, 1(2), 225-247. https://doi.org/10.5802/alco.13
Bjorner, A., & Brenti, F. (2006). Combinatorics of Coxeter groups (Vol. 231). Springer Science & Business Media.
Garsia, A. M., & Procesi, C. (1992). On certain graded sn-modules and the q-kostka polynomials. Advances in Mathematics, 94(1), 82-138. https://doi.org/10.1016/0001-8708(92)90034-I
Macdonald, I. G. (1991). Notes on Schubert polynomials (Vol. 6). Montréal: Dép. de mathématique et d'informatique, Université du Québec à Montréal.
Mbirika, A. (2010). A Hessenberg generalization of the Garsia-Procesi basis for the cohomology ring of Springer varieties. The Electronic Journal of Combinatorics, 17(1), 153. https://doi.org/10.37236/425
Precup, M., & Tymoczko, J. (2019). Springer fibers and Schubert points. European Journal of Combinatorics, 76, 10-26. https://doi.org/10.1016/j.ejc.2018.08.010
Sagan, B. E. (2013). The symmetric group: representations, combinatorial algorithms, and symmetric functions (Vol. 203). Springer Science & Business Media.
Tymoczko, J. (2016). The geometry and combinatorics of Springer fibers. arXiv preprint arXiv:1606.02760. https://doi.org/10.1090/conm/691/13903
Tymoczko, J. S. (2006). Linear conditions imposed on flag varieties. American Journal of Mathematics, 128(6), 1587-1604. https://doi.org/10.1353/ajm.2006.0050
This work is licensed under a Creative Commons Attribution 4.0 International License.