A121152 Dimension of the space spanned by the symmetric functions L_lambda of Gessel and Reutenauer, where lambda ranges over all partitions of n.

1, 1, 2, 3, 4, 6, 10, 13, 19, 26, 38, 52, 70, 91, 123, 161

Offset

0,3

References

R. P. Stanley, Enumerative Combinatorics, vol. 2 (Exercise 7.89).

Links

Table of n, a(n) for n=0..15.

I. M. Gessel and C. Reutenauer, Counting permutations with given cycle structure and descent set, J. Combin. Theory, Ser. A, 64, 1993, 189-215.

Example

In terms of Schur functions we have:
  L[4] = s[3,1] + s[2,1,1],
  L[3,1] = s[3,1] + s[2,2] + s[1,1,1,1],
  L[2,2] = s[2,2] + s[1,1,1,1],
  L[2,1,1] = s[3,1] + s[2,1,1],
  L[4] = s[4].
There is one linear dependence relation, viz., L[4] = L[2,1,1],
so for n=4 we get the value 5-1=4.

Crossrefs

Sequence in context: A061018 A130126 A288338 * A229863 A215255 A200928

Adjacent sequences: A121149 A121150 A121151 * A121153 A121154 A121155

Keyword

nonn,more

Author

Richard Stanley, Aug 12 2006

Status

approved