Solid Partition
Solid partitions are generalizations of Plane Partitions. MacMohan (1960) conjectured the GeneratingFunction for the number of solid partitions was
but this was subsequently shown to disagree at
(Atkin et al. 1967). Knuth (1970) extended the tabulation of values, but was unable to finda correct generating function. The first few values are 1, 4, 10, 26, 59, 140, ... (Sloane's A000293).
References
Atkin, A. O. L.; Bratley, P.; MacDonald, I. G.; and McKay, J. K. S. ``Some Computations for Knuth, D. E. ``A Note on Solid Partitions.'' Math. Comput. 24, 955-961, 1970. MacMahon, P. A. ``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 Partitions in Three-Dimensional Space.'' Phil. Trans. Roy. Soc. London Ser. A 211, 345-373, 1912b. MacMahon, P. A. Combinatory Analysis, Vol. 2. New York: Chelsea, pp. 75-176, 1960. Sloane, N. J. A. SequenceA000293/M3392in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
-Dimensional Partitions.'' Proc. Cambridge Philos. Soc. 63, 1097-1100, 1967.
- Scalene Triangle
- Scaling
- Scattering Operator
- Scattering Theory
- Schaar's Identity
- Schanuel's Conjecture
- Schauder Fixed Point Theorem
- Scheme
- Schensted Correspondence
- Scherk's Minimal Surfaces
- Schiffler Point
- Schinzel Circle
- Schinzel's Hypothesis
- Schinzel's Theorem
- Schisma
- Schlegel Graph
- Schläfli Double Six
- Schläfli Function
- Schläfli Integral
- Schläfli Polynomial
- Schläfli's Formula
- Schläfli's Modular Form
- Schläfli Symbol
- Schlömilch's Function
- Schlömilch's Series