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 A130715 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. 0

%I #8 Oct 18 2020 13:59:35

%S 1,2,7,40,358,4884,99665,3000736,131932016,8403206128

%N 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.

%C It is easy to mistake these for monotone triangles.

%H Luca De Feo, David Jao and Jerome Plut, <a href="https://eprint.iacr.org/2011/506">Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies</a>, Cryptology ePrint Archive: Report 2011/506. - From _N. J. A. Sloane_, Dec 22 2012

%e a(3)=7 because the vertices of GT(3) are

%e 123

%e 12

%e 1

%e ---

%e 123

%e 12

%e 2

%e ---

%e 123

%e 13

%e 1

%e ---

%e 123

%e 13

%e 3

%e ---

%e 123

%e 23

%e 2

%e ---

%e 123

%e 23

%e 3

%e ---

%e 123

%e 22

%e 2

%e ---

%t (* 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]]

%K nonn,more

%O 1,2

%A David E Speyer (speyer(AT)post.harvard.edu), Jul 02 2007

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Last modified August 4 22:06 EDT 2024. Contains 374934 sequences. (Running on oeis4.)