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Search: id:A059760
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| A059760 |
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a(n) is the number of edges (one-dimensional faces) in the convex polytope of real n X n doubly stochastic matrices. The vertices are the n! permutation matrices. If A(p1) and A(p2) are two permutation matrices corresponding to permutations p1 and p2 the closed interval between these two matrices forms an edge of the polytope iff the permutation p1*(p2^-1) is a cycle, i.e. its cycle decomposition in the symmetric group S_n contains exactly one nontrivial cycle. |
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12
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| 0, 1, 15, 240, 5040, 147240, 5959800, 323850240, 22800476160, 2017745251200, 219066851203200, 28615863103027200, 4425987756321331200, 799788468703877452800, 166940001463941433728000
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OFFSET
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0,3
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FORMULA
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a(n) = 1/2* n! * (Sum k=2...n C(n, k)*(k-1)!)
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EXAMPLE
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a(3) = 15 because there are 3! = 6 vertices and C(6,2) intervals and in this case all are edges so a(3) = C(6,2) = 15
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MAPLE
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with(combinat): for n from 1 to 30 do printf(`%d, `, 1/2* n! * sum(binomial(n, k)*(k-1)!, k=2..n)) od:
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CROSSREFS
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Cf. A059615.
Note that b(n) = (Sum k=2...n C(n, k)*(k-1)!) gives sequence A006231.
Sequence in context: A090411 A154806 A133199 this_sequence A059615 A163031 A065920
Adjacent sequences: A059757 A059758 A059759 this_sequence A059761 A059762 A059763
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KEYWORD
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nonn
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AUTHOR
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Noam Katz (noamkj(AT)hotmail.com), Feb 20 2001
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 21 2001
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