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A120421 Number of distinct ribbon Schur functions with n boxes; also the number of distinct multisets of partitions determined by all coarsenings of compositions of n. 0

%I

%S 1,2,3,6,10,20,36,72,135,272,528,1052,2080,4160,8244,16508,32896,

%T 65770,131328,262632,524744,1049600,2098176,4196200,8390620,16781312,

%U 33558291,67116944,134225920,268451240,536887296,1073774376,2147515424

%N Number of distinct ribbon Schur functions with n boxes; also the number of distinct multisets of partitions determined by all coarsenings of compositions of n.

%D Louis Billera, Hugh Thomas and Stephanie van Willigenburg "Decomposable compositions, symmetric quasisymmetric functions and equality of ribbon Schur functions" Adv. Math. 204: 204-240 (2006).

%H Louis Billera, Hugh Thomas and Stephanie van Willigenburg <a href="http://arXiv.org/abs/math.CO/0405434">"Decomposable compositions, symmetric quasisymmetric functions and equality of ribbon Schur functions"</a> Adv. Math. 204: 204-240 (2006).

%H M. Rubey, <a href="http://arxiv.org/abs/1008.2501">The number of ribbon Schur functions</a> [From Martin Rubey (martin.rubey(AT)math.uni-hannover.de), Aug 17 2010]

%F Dirichlet G.f.: 2 C(s) S(s)/(C(s)+S(s)) where C(s)=Sum_{n>0} 2^{n-1} n^{-s} and S(s)=Sum_{n>0} 2^{floor(n/2)} n^{-s} [From Martin Rubey (martin.rubey(AT)math.uni-hannover.de), Aug 17 2010]

%e a(4)=6 as the multisets are {4}, {4,31}, {4,22}, {4,31,22,211}, {4,31,31,211} and {4,31,31,22,211,211,211,1111}

%Y Cf. A005418.

%K nonn

%O 1,2

%A Stephanie van Willigenburg (steph(AT)math.ubc.ca), Jul 09 2006

%E Corrected and extended by Martin Rubey (martin.rubey(AT)math.uni-hannover.de), Aug 17 2010

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Last modified December 2 15:00 EST 2022. Contains 358510 sequences. (Running on oeis4.)