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Search: id:A115868
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| A115868 |
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Invariants for a hidden action of S_(n+1) on Cayley trees with n vertices. |
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1
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| 1, 1, 1, 1, 2, 2, 4, 6, 11, 18, 39, 70, 153, 321, 721, 1612, 3792, 8896, 21498, 52230, 128994, 320786, 806582
(list; graph; listen)
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OFFSET
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2,5
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COMMENT
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This is the multiplicity of the trivial module in a sequence of modules of dimension (n-1)^(n-3) over the symmetric groups S_n. The restriction of these modules to S_(n-1) is given by the action on trees.
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FORMULA
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no simple formula known, only a complicated sum over partitions
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EXAMPLE
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M[6]=s[2, 1, 1, 1, 1] + 3 s[2, 2, 2] + 2 s[3, 1, 1, 1] + 2 s[3, 2, 1] + s[4, 1, 1] + 4 s[4, 2] + s[5, 1] + 2 s[6] as a sum of Schur functions hence a[6]=2.
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CROSSREFS
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Cf. A000055 and A000272.
Sequence in context: A124346 A033961 A000672 this_sequence A103299 A154779 A010101
Adjacent sequences: A115865 A115866 A115867 this_sequence A115869 A115870 A115871
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KEYWORD
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nonn
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AUTHOR
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F. Chapoton (fchapoton(AT)voila.fr), Mar 14 2006
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