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%I #7 Feb 11 2023 12:34:05
%S 1,2,3,4,7,9,11,17,23,28,39,48,59,79,100,121,152,185,225,280,338,404,
%T 492,584,696,835,983,1162,1385,1612
%N Number of monomial ideals in two variables that are artinian, integrally closed and of colength n.
%C 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.
%D G. E. Andrews, The Theory of Partitions, Addison-Wesley Publishing Company, 1976.
%D M. Paulsen & J. Snellman, Enumerativa egenskaper hos konkava partitioner (in Swedish), Department of Mathematics, Stockholm University.
%H V. Crispin Quinonez, <a href="https://www2.math.su.se/reports/2002/7/2002-7.pdf">Integrally closed monomial ideals and powers of ideals</a>, Research Reports in Mathematics Number 7 2002, Department of Mathematics, Stockholm University.
%e 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.
%Y Cf. A086161, A086162, A086163.
%K hard,nonn
%O 0,2
%A Jan Snellman and Michael Paulsen (Jan.Snellman(AT)math.su.se), Jul 03 2003
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