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A restricted growth function (RGF) of length n is a sequence w=w1w2…wn of positive integers such that w1=1 and wi≤1+max{w1,…,wi−1} for i≥2. RGFs are of interest because they are in natural bijection with set partitions of {1,2,…,n}. An RGF w avoids another RGF v if there is no subword of w which standardizes to v. We study the generating functions ∑w∈Rn(v)qst(w) where Rn(v) is the set of RGFs of...
A set partition σ of [n]={1,…,n} contains another set partition π if restricting σ to some S⊆[n] and then standardizing the result gives π. Otherwise we say σ avoids π. For all sets of patterns consisting of partitions of [3], the sizes of the avoidance classes were determined by Sagan and by Goyt. Set partitions are in bijection with restricted growth functions (RGFs) for which Wachs and White defined...
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