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比利时vs摩洛哥足彩 ,
university of california san diego

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math 269 - combinatorics

angela hicks

ucsd

parking function bijection suggested by the haglund-morse-zabrocki conjecture

abstract:

in recent work jim haglund, jennifer morse and mike zabrocki introduce a new statistic on parking functions, the ``diagonal composition,'' which gives the lengths of the intervals between successive diagonal hits of the dyck path. they conjectured that the nabla operator, when applied to certain modified hall-littlewood functions indexed by compositions, yields the weighted sum of the corresponding parking functions by area, dinv, and gessel quasisymmetric function. this conjecture then gives a sharpening of the ``shuffle conjecture'' and suggests several combinatorial conjectures about the parking functions. in particular, we discuss a bijective map on the parking functions implied by the commutativity properties of the modified hall-littlewood polynomials that appear in their conjecture.

november 23, 2010

3:00 pm

ap&m 7321

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