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 A357592 Number of edges of the Minkowski sum of n simplices with vertices e_(i+1), e_(i+2), e_(i+3) for i=0,...,n-1, where e_i is a standard basis vector. 0

%I #8 Nov 19 2022 14:08:00

%S 3,11,34,96,260,683,1757,4447,11114,27493

%N Number of edges of the Minkowski sum of n simplices with vertices e_(i+1), e_(i+2), e_(i+3) for i=0,...,n-1, where e_i is a standard basis vector.

%H L. Escobar, P. Gallardo, J. González-Anaya, J. L. González, G. Montúfar, and A. H. Morales, <a href="https://arxiv.org/abs/2209.14978">Enumeration of max-pooling responses with generalized permutohedra</a>, arXiv:2209.14978 [math.CO], 2022. (See Table 2)

%o (Sage) def a(n): return len(PP(n,3,1).graph().edges())

%o def Delta(I,n):

%o IM = identity_matrix(n)

%o return Polyhedron(vertices=[IM[e] for e in I],backend='normaliz')

%o def Py(n,SL,yL):

%o return sum(yL[i]*Delta(SL[i],n) for i in range(len(SL)))

%o def PP(n,k,s):

%o SS = [set(range(s*i,k+s*i)) for i in range(n)],[1,]*(n)

%o return Py(s*(n-1)+k,SS[0],SS[1])

%o [a(n) for n in range(1,4)]

%Y Cf. A033303, A007070.

%K nonn,hard,more

%O 1,1

%A _Alejandro H. Morales_, Oct 05 2022

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Last modified August 7 05:36 EDT 2024. Contains 375008 sequences. (Running on oeis4.)