A note on solid partitions

Author:
Donald E. Knuth

Journal:
Math. Comp. **24** (1970), 955-961

MSC:
Primary 05.10; Secondary 10.00

DOI:
https://doi.org/10.1090/S0025-5718-1970-0277401-7

MathSciNet review:
0277401

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

**[1]**A. O. L. Atkin, P. Bratley, I. G. Macdonald, and J. K. S. McKay,*Some computations for 𝑚-dimensional partitions*, Proc. Cambridge Philos. Soc.**63**(1967), 1097–1100. MR**0217029****[2]**Edward A. Bender and Donald E. Knuth,*Enumeration of plane partitions*, J. Combinatorial Theory Ser. A**13**(1972), 40–54. MR**0299574****[3]**Donald E. Knuth,*The art of computer programming*, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975. Volume 1: Fundamental algorithms; Addison-Wesley Series in Computer Science and Information Processing. MR**0378456****[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]**Percy A. MacMahon,*Combinatory analysis*, Two volumes (bound as one), Chelsea Publishing Co., New York, 1960. MR**0141605**

Retrieve articles in *Mathematics of Computation*
with MSC:
05.10,
10.00

Retrieve articles in all journals with MSC: 05.10, 10.00

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0277401-7

Keywords:
Plane partitions,
solid partitions,
partially-ordered partitions,
partiallyordered permutations,
index of permutation,
backtracking

Article copyright:
© Copyright 1970
American Mathematical Society