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math.CO2012★ 1 cited
A three shuffle case of the compositional parking function conjecture
Adriano M. Garsia, Guoce Xin, Mike Zabrocki
We prove here that the polynomial <nabla(C_p(1)), e_a h_b h_c> q, t-enumerates, by the statistics dinv and area, the parking functions whose supporting Dyck path touches the main d…
math.CO2012
A new `dinv' arising from the two part case of the Shuffle Conjecture
Adrian Duane, Adriano M. Garsia, Mike Zabrocki
In a recent paper J. Haglund showed that a certain symmetric function expresion enumerates by t^{area} q^{dinv} of the parking functions whose diagonal word is in the shuffle of 12…