Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Strange Expectations and Simultaneous Cores
Marko Thiel  1  , Nathan Williams  2  
1 : Institut für Mathematik, Universität Zürich, Zürich
2 : Laboratoire de combinatoire et d'Informatique mathématique [Montréal]  (LaCIM)  -  Website
LaCIM Pavillon Président-Kennedy 201 CP 8888, Succ. Centre-ville Montréal (Québec) H3C 3P8 -  Canada

Let gcd(a, b) = 1. J. Olsson and D. Stanton proved that the maximum number of boxes in a simultaneous (a, b)-core is (a2 1)(b2 1) 24, and showed that this maximum is achieved by a unique core. P. Johnson combined Ehrhart theory with the polynomial method to prove D. Armstrong's conjecture that the expected number of boxes in a simultaneous (a, b)-core is (a−1)(b−1)(a+b+1) 24. We apply P. Johnson's method to compute the variance and third moment. By extending the definitions of “simultaneous cores” and “number of boxes” to affine Weyl groups, we give uniform generalizations of these formulae to simply-laced affine types. We further explain the appearance of the number 24 using the “strange formula” of H. Freudenthal and H. de Vries. 

  • Poster
Online user: 1