Demonstrates the induction of classical parking spaces to the hyperoctahedral group, suggesting new connections in combinatorial theory.
The permutation module Parkn of Symn acting on parking functions of length n appears in the decomposition of the space of diagonal coinvariants. This paper concerns the induction of the classical parking space to the hyperoctahedral group Bn, dubbed SParkn. We describe a set of generalized parking functions whose permutation module over Bn coincides with this induction. Additionally, we introduce a generalization of Kreweras numbers giving the expansion of the Frobenius character of SParkn in the hμ(x)hν(y) basis.
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Harris et al. (2026) studied this question.
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