RSK tableaux and the weak orderon fully commutative permutations
Abstract
For each fully commutative permutation, we construct a “boolean core,” which is the maximal boolean permutation in its principal order ideal under the right weak order. We partition the set of fully commutative permutations into the recently defined crowded and uncrowded elements, distinguished by whether or not their RSK insertion tableaux satisfy a sparsity condition. We show that a fully commutative element is uncrowded exactly when it shares the RSK insertion tableau with its boolean core. We present the dynamics of the right weak order on fully commutative permutations, with particular interest in when they change from uncrowded to crowded. In particular, we use consecutive permutation patterns and descents to characterize the minimal crowded elements under the right weak order.
Document Type
Article
Publication Date
12-1-2023
Publisher Statement
© The authors. Released under the CC BY-ND license (International 4.0)
Recommended Citation
Gunawan, E., Pan, J., Russell, H. M., & Tenner, B. (2023). RSK tableaux and the weak order on fully commutative permutations. Electronic Journal of Combinatorics, 30(4). https://www.combinatorics.org/ojs/index.php/eljc/article/view/v30i4p33/pdf