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A352457
Codimension of Lyndon symmetric functions of degree n.
0
0, 0, 0, 1, 1, 1, 2, 3, 4, 4, 4, 7, 10, 12, 15
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
Cf. A000041.
Sequence in context: A076410 A361164 A309941 * A211509 A305594 A320778
KEYWORD
nonn,more
AUTHOR
Richard Stanley, Mar 16 2022
STATUS
approved