2015/04/26 by Rhoades, Brendon
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1504.06869
Let W be an irreducible real reflection group. Armstrong, Reiner, and the author presented a model for parking functions attached to W and made three increasingly strong conjectures about these objects. The author generalized these objects and conjectures to the Fuss-Catalan level of generality. Even the weakest of these conjectures would imply a collection of facts in Coxeter-Catalan theory which are at present understood only in a case-by-case fashion. We prove that when W belongs to any the infinite families ABCDI, the strongest of these conjectures is generically true.