A352457 Codimension of Lyndon symmetric functions of degree n.

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.

Links

Table of n, a(n) for n=1..15.

Crossrefs

Cf. A000041.

Sequence in context: A076410 A361164 A309941 * A211509 A305594 A320778

Adjacent sequences: A352454 A352455 A352456 * A352458 A352459 A352460

Keyword

nonn,more

Author

Richard Stanley, Mar 16 2022

Status

approved