editing

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editing

Also the number of commutation classes of reduced words for the longest element of a Weyl group of type A_{n-1} (see Armstrong reference).

approved

A projective reflection product on a set S is irreducible if S cannot be written as the disjoint union of two subsets X and Y such that x*y=y and y*x=x for all x in X and y in Y.

The definition of an irreducible reflection product is that for every x in the set there exists a y in the set such that x*y is not equal to y.

Define i(0)=0 and let i(p) to be the number of irreducible projective reflection products on a set with p elements. Define c(p,1)=i(p) and recursively define c(p,q)=sum(k=0 to p) of binomial(p,k)*i(k)*c(p-k,q-1). Then a(n)=sum(k=1 to n) of c(n,k)/k!.

1, 1, 3, 15, 75, 495, 3465, 26145, 250425, 2601585, 27785835, 335269935, 4390941555, 61068182175, 944855136225, 15284321877825, 255796481365425, 4593387354581025, 87705978094609875, 1756845938220548175, 36984305562685155675, 813838622859091004175, 18688518954270224084025, 450078776141006938550625, 11274055003691154725675625

allocated for Matthew J. Samuel

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