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A200580
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Sum of dimension exponents of supercharacter of unipotent upper triangular matrices.
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2
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0, 1, 10, 73, 490, 3246, 21814, 150535, 1072786, 7915081, 60512348, 479371384, 3932969516, 33392961185, 293143783762, 2658128519225, 24872012040510, 239916007100054, 2383444110867378, 24363881751014383, 256034413642582418, 2763708806499744097
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OFFSET
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1,3
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COMMENTS
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Supercharacter theory of unipotent upper triangular matrices over a finite field F(2) is indexed by set partitions S(n) of {1,2,..., n} where a set partition P of {1,2,..., n} is a subset { (i,j) : 1 <= i < j <= n}
such that (i,j) in P implies (i,k),(k,j) are not in P for all i<l<j.
The dimension of the representation associated to the supercharacter indexed by P is given by 2^Dim(P) where Dim(P) = sum [ j-i , (i,j) in P ].
The sequence we have is a(n) = sum [ Dim(P) , P in S(n) ].
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REFERENCES
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C. Andre, Basic characters of the unitriangular group, Journal of algebra, 175 (1995), 287-319.
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LINKS
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Table of n, a(n) for n=1..22.
M. Aguiar, C. Andre, C. Benedetti, N. Bergeron, Z. Chen, P. Diaconis, A. Hendrickson, S. Hsiao, I.M. Isaacs, A. Jedwab, K. Johnson, G. Karaali, A. Lauve, T. Le, S. Lewis, H. Li, K. Magaard, E. Marberg, J-C. Novelli, A. Pang, F. Saliola, L. Tevlin, J-Y. Thibon, N. Thiem, V. Venkateswaran, C.R. Vinroot, N. Yan, M. Zabrocki, Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
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MAPLE
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b:=proc(n, k) option remember;
if n=1 and k=1 then RETURN(1) fi;
if k=1 then RETURN(b(n-1, n-1)) fi;
b(n, k-1)+b(n-1, k-1)
end:
a:=proc(n) local res, k;
res:=0;
for k to n-1 do res:=res+k*(n-k)*b(n, k) od;
res
end:
seq(a(n), n=1..34);
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CROSSREFS
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Cf. A011971 (sequence is computed from the Aitken's array b(n,k)
a(n) = sum [ k*(n-k)*b(n,k), k=1..n-1 ]).
Cf. A200660, A200673 (other statistics related to supercharacter theory).
Sequence in context: A161743 A016211 A055424 * A181678 A206817 A159687
Adjacent sequences: A200577 A200578 A200579 * A200581 A200582 A200583
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KEYWORD
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nonn
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AUTHOR
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Nantel Bergeron, Nov 19 2011
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STATUS
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approved
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