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no. 5
Strange expectations in affine Weyl groups
Stucky, Eric Nathan1; Thiel, Marko2; Williams, Nathan3
1 Charles University Faculty of Mathematics and Physics Department of Algebra Sokolovska 83 18600 Praha 8 Czech Republic
2 Unaffiliated
3 University of Texas at Dallas Mathematical Sciences FO 2.402C 800 W. Campbell Rd. Richardson, TX 75080
Algebraic Combinatorics, Volume 7 (2024) no. 5, pp. 1551-1574.

Our main result is a generalization, to all affine Weyl groups, of P. Johnson’s proof of D. Armstrong’s conjecture for the expected number of boxes in a simultaneous core. This extends earlier results by the second and third authors in simply-laced type. We do this by modifying and refining the appropriate notion of the “size” of a simultaneous core. In addition, we provide combinatorial core-like models for the coroot lattices in classical type and type G 2 .

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.383
Classification: 05E15, 20F55, 13F60
Keywords: affine Weyl groups, core partitions, Ehrhart theory, root systems

Stucky, Eric Nathan 1; Thiel, Marko 2; Williams, Nathan 3

1 Charles University Faculty of Mathematics and Physics Department of Algebra Sokolovska 83 18600 Praha 8 Czech Republic
2 Unaffiliated
3 University of Texas at Dallas Mathematical Sciences FO 2.402C 800 W. Campbell Rd. Richardson, TX 75080
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Stucky, Eric Nathan; Thiel, Marko; Williams, Nathan. Strange expectations in affine Weyl groups. Algebraic Combinatorics, Volume 7 (2024) no. 5, pp. 1551-1574. doi : 10.5802/alco.383. https://alco.centre-mersenne.org/articles/10.5802/alco.383/

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