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A note on solid partitions

Author: Donald E. Knuth
Journal: Math. Comp. 24 (1970), 955-961
MSC: Primary 05.10; Secondary 10.00
MathSciNet review: 0277401
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Abstract: The problem of enumerating partitions which satisfy a given partial order relation is reduced to the problem of enumerating permutations satisfying that relation. This theorem is applied to the enumeration of solid partitions; existing tables of solid partitions are extended.

References [Enhancements On Off] (What's this?)

  • [1] A. O. L. Atkin, P. Bratley, I. G. MacDonald & J. K. S. McKay, "Some computations for $ m$-dimensional partitions," Proc. Cambridge Philos. Soc., v. 63, 1967, pp. 1097-1100. MR 36 #124. MR 0217029 (36:124)
  • [2] Edward A. Bender & Donald E. Knuth, "Enumeration of plane partitions," J. Combinatorial Theory. (To appear.) MR 0299574 (45:8622)
  • [3] Donald E. Knuth, The Art of Computer Programming. Vol. 1, Addison-Wesley, Reading, Mass., 1968. MR 0378456 (51:14624)
  • [4] Major P. A. MacMahon, "Memoir on the theory of the partitions of numbers. V: Partitions in two-dimensional space," Philos. Trans. Roy. Soc London Ser. A, v. 211, 1912, pp. 75-110.
  • [5] Major P. A. MacMahon, "Memoir on the theory of the partitions of numbers. VI: Partitions in two-dimensional space, to which is added an adumbration of the theory of the partitions in three-dimensional space," Philos. Trans. Roy. Soc. London Ser. A, v. 211, 1912, pp. 345-373.
  • [6] Major P. A. MacMahon, Combinatory Analysis. Vol. 2, Cambridge Univ. Press, Cambridge, 1916; reprint, Chelsea, New York, 1960. MR 0141605 (25:5003)

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Keywords: Plane partitions, solid partitions, partially-ordered partitions, partiallyordered permutations, index of permutation, backtracking
Article copyright: © Copyright 1970 American Mathematical Society

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