A352457 Codimension of Lyndon symmetric functions of degree n.

0, 0, 0, 1, 1, 1, 2, 3, 4, 4, 4, 7, 10, 12, 15, 24, 27, 31, 40, 50, 59, 78

Offset: 1

Author

Richard Stanley, Mar 16 2022

Keywords

• nonn
• more

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.

Extensions

More terms from Ira M. Gessel, Mar 20 2025