OFFSET
1,7
COMMENTS
For each partition p of n, there is a "Lyndon symmetric function" L_p which is homogeneous of degree n. The Q-vector space V_n spanned by all Lyndon symmetric functions of degree n is a subspace of the space Lambda^n of all homogeneous symmetric functions over Q of degree n, which has dimension p(n), the number of partitions of n (A000041). Then a(n) is the codimension of V_n in Lambda^n.
REFERENCES
R. Stanley, Enumerative Combinatorics, volume 2, Exercise 7.89.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Richard Stanley, Mar 16 2022
STATUS
approved