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A130715
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Number of vertices of the Gelfand Tsetlin-polytope. Alternatively, the number of Gelfand-Tsetlin patterns with top row 1234...n and such that every entry in a given row also appears in the row above it.
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0
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OFFSET
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1,2
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COMMENTS
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It is easy to mistake these for monotone triangles.
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LINKS
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EXAMPLE
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a(3)=7 because the vertices of GT(3) are
123
12
1
---
123
12
2
---
123
13
1
---
123
13
3
---
123
23
2
---
123
23
3
---
123
22
2
---
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MATHEMATICA
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(* G computes the required sequence, F computes the similar sequence with any monotone sequence permitted as the input top row. Note that F and Bifurcate cache their values. *) Bifurcate[l_] := Bifurcate[l] = If[Length[l] == 1, { {} }, Union[Map[Prepend[ #, l[[1]]] &, Bifurcate[Drop[l, 1]]], Map[ Prepend[ #, l[[2]]] &, Bifurcate[Drop[l, 1]]]]] F[l_] := F[l] = If[Length[l] == 0, 1, Apply[Plus, Map[F, Bifurcate[l]]]] G[n_] := F[Range[n]]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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David E Speyer (speyer(AT)post.harvard.edu), Jul 02 2007
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STATUS
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approved
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