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A084913 Number of monomial ideals in two variables that are artinian, integrally closed and of colength n. 3
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 (list; graph; refs; listen; history; text; internal format)



Alternatively, "concave partitions" of n, where a concave partition is defined by demanding that the monomial ideal, generated by the monomials whose exponents do no lie in the Ferrers diagram of the partition, is integrally closed.


G. E. Andrews, The Theory of Partitions, Addison-Wesley Publishing Company, 1976.

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

M. Paulsen & J. Snellman, Enumerativa egenskaper hos konkava partitioner (in Swedish), Department of Mathematics, Stockholm University.


Table of n, a(n) for n=0..29.


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.


Cf. A086161, A086162, A086163.

Sequence in context: A023546 A236337 A191989 * A270839 A117450 A132381

Adjacent sequences:  A084910 A084911 A084912 * A084914 A084915 A084916




Jan Snellman and Michael Paulsen (Jan.Snellman(AT)math.su.se), Jul 03 2003



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Last modified January 16 06:48 EST 2021. Contains 340204 sequences. (Running on oeis4.)