A084913 Number of monomial ideals in two variables that are Artinian, integrally closed and of colength n.

1, 2, 3, 4, 7, 9, 11, 17, 23, 28, 39, 48, 59, 79, 100, 121, 152, 185, 225, 280, 338, 404, 492, 584, 696, 835, 983, 1162, 1385, 1612

Offset: 0

Author

Jan Snellman and Michael Paulsen, Jul 03 2003

Keywords

• hard
• nonn
• more

Comments

Alternatively, "concave partitions" of n, where a concave partition is defined by demanding that the monomial ideal, generated by the monomials whose exponents do not lie in the Ferrers diagram of the partition, is integrally closed.

Examples

			a(4) = 4 because the Artinian monomial ideals in two variables that have colength 4 are (x^4,y), (x^3,y^2), (x^2, y^2), (x^2,xy,y^3), (x,y^4), corresponding to the partitions (1,1,1,1), (3,1), (2,2), (2,1,1), (4); the ideal (x^2,y^2) is not integrally closed, hence the partition (2,2) is not concave.
		

References

• G. E. Andrews, The Theory of Partitions, Addison-Wesley Publishing Company, 1976.
• M. Paulsen & J. Snellman, Enumerativa egenskaper hos konkava partitioner (in Swedish), Department of Mathematics, Stockholm University.

Links

• V. Crispin Quinonez, Integrally closed monomial ideals and powers of ideals, Research Reports in Mathematics Number 7 2002, Department of Mathematics, Stockholm University.

Crossrefs

Cf. A086161, A086162, A086163.