Maximizing the Edelman-Greene statistic
| Autor: | Orelowitz, Gidon |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | The $\textit{Edelman-Greene statistic}$ of S. Billey-B. Pawlowski measures the "shortness" of the Schur expansion of a Stanley symmetric function. We show that the maximum value of this statistic on permutations of Coxeter length $n$ is the number of involutions in the symmetric group $S_n$, and explicitly describe the permutations that attain this maximum. Our proof confirms a recent conjecture of C. Monical, B. Pankow, and A. Yong: we give an explicit combinatorial injection between a certain collections of Edelman-Greene tableaux and standard Young tableaux. Comment: 9 Pages |
| Databáze: | arXiv |
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