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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