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A121152 Dimension of the space spanned by the symmetric functions L_lambda of Gessel and Reutenauer, where lambda ranges over all partitions of n. 0
1, 1, 2, 3, 4, 6, 10, 13, 19, 26, 38, 52, 70, 91, 123, 161 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

I. M. Gessel and C. Reutenauer, J. Combinatorial Theory (A) 64 (1993), 189-215.

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

LINKS

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

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

AUTHOR

Richard Stanley, Aug 12 2006

STATUS

approved

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Last modified June 19 22:51 EDT 2021. Contains 345152 sequences. (Running on oeis4.)