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A084913
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Number of monomial ideals in two variables that are artinian, integrally closed and of colength n.
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3
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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
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OFFSET
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0,2
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COMMENTS
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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.
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=0..29.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A086161, A086162, A086163.
Sequence in context: A023546 A236337 A191989 * A270839 A117450 A132381
Adjacent sequences: A084910 A084911 A084912 * A084914 A084915 A084916
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KEYWORD
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hard,nonn
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AUTHOR
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Jan Snellman and Michael Paulsen (Jan.Snellman(AT)math.su.se), Jul 03 2003
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STATUS
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approved
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