A new “dinv” arising from the two part case of the shuffle conjecture
Journal of Algebraic Combinatorics, Volume 37, Issue 4, 2012.
Symmetric functionsMacdonald polynomialsParking functions
For a symmetric function , the eigen-operator Δ acts on the modified Macdonald basis of the ring of symmetric functions by . In a recent paper (Int. Math. Res. Not. 11:525–560, ), J. Haglund showed that the expression ,-enumerates the parking functions whose diagonal word is in the shuffle 12⋯∪∪+1⋯+ with of the cars +1,…,+ in the main d...More
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