On the Inversion and Dimension Pairs of Row-Strict Tableaux

Authors

  • Felemu Olasupo Department of Mathematical Science, Adekunle Ajasin University, Akungba Akoko, Ondo State, Nigeria
  • Adetunji Patience Department of Mathematics, University of Lagos, Akoka, Yaba,Lagos, Nigeria

DOI:

https://doi.org/10.3126/jnms.v7i1.67485

Keywords:

Flag variety, Springer variety, Standard tableaux, Row-strict tableaux, Betti numbers

Abstract

In this article, we consider two algorithms, dimension and inversion pairs of rows-strict, used for the computation of Betti numbers of Springer varieties and then show that the sequences respectively generated by these algorithms are dual to each other, (except for λ = 1n where Ik = Dk) and that the sum Ik + Dk gives another sequence which is palindromic. We also show that for each row-strict tableau τ of shape λ = n − r, 1r (0 ≤ r ≤ n − 1), the dimension of the corresponding Springer varieties equals the cardinality of the union of the set of inversions and dimensions of τ. This research contributes to a deeper understanding of the rich combinatorial landscape of tableaux, opening up new avenues for further research.

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Published

2024-07-04

How to Cite

Olasupo, F., & Patience, A. (2024). On the Inversion and Dimension Pairs of Row-Strict Tableaux. Journal of Nepal Mathematical Society, 7(1), 32–39. https://doi.org/10.3126/jnms.v7i1.67485

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Articles