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1: 26.2 Basic Definitions
Partition
As an example, { 1 , 3 , 4 } , { 2 , 6 } , { 5 } is a partition of { 1 , 2 , 3 , 4 , 5 , 6 } . … The total number of partitions of n is denoted by p ( n ) . …For the actual partitions ( π ) for n = 1 ( 1 ) 5 see Table 26.4.1. The integers whose sum is n are referred to as the parts in the partition. …
2: 26.10 Integer Partitions: Other Restrictions
§26.10 Integer Partitions: Other Restrictions
§26.10(i) Definitions
§26.10(ii) Generating Functions
§26.10(vi) Bessel-Function Expansion
3: 26.12 Plane Partitions
§26.12 Plane Partitions
§26.12(i) Definitions
The plane partition in Figure 26.12.1 is an example of a cyclically symmetric plane partition. …
§26.12(ii) Generating Functions
4: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
§26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
Table 26.4.1 gives numerical values of multinomials and partitions λ , M 1 , M 2 , M 3 for 1 m n 5 . … λ is a partition of n : … M 3 is the number of set partitions of { 1 , 2 , , n } with a 1 subsets of size 1, a 2 subsets of size 2, , and a n subsets of size n : …
§26.4(ii) Generating Function
5: 26.9 Integer Partitions: Restricted Number and Part Size
p k ( n ) denotes the number of partitions of n into at most k parts. See Table 26.9.1. … It follows that p k ( n ) also equals the number of partitions of n into parts that are less than or equal to k . …
§26.9(ii) Generating Functions
6: Bibliography C
  • N. Calkin, J. Davis, K. James, E. Perez, and C. Swannack (2007) Computing the integer partition function. Math. Comp. 76 (259), pp. 1619–1638.
  • R. Chelluri, L. B. Richmond, and N. M. Temme (2000) Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.
  • M. Colman, A. Cuyt, and J. Van Deun (2011) Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
  • Combinatorial Object Server (website) Department of Computer Science, University of Victoria, Canada.
  • M. D. Cooper, R. H. Jeppesen, and M. B. Johnson (1979) Coulomb effects in the Klein-Gordon equation for pions. Phys. Rev. C 20 (2), pp. 696–704.
  • 7: Bibliography R
  • H. Rademacher (1938) On the partition function p(n). Proc. London Math. Soc. (2) 43 (4), pp. 241–254.
  • S. Ramanujan (1921) Congruence properties of partitions. Math. Z. 9 (1-2), pp. 147–153.
  • H. E. Rauch and A. Lebowitz (1973) Elliptic Functions, Theta Functions, and Riemann Surfaces. The Williams & Wilkins Co., Baltimore, MD.
  • J. Raynal (1979) On the definition and properties of generalized 6 - j  symbols. J. Math. Phys. 20 (12), pp. 2398–2415.
  • RISC Combinatorics Group (website) Research Institute for Symbolic Computation, Hagenberg im Mühlkreis, Austria.
  • 8: Bibliography W
  • E. L. Wachspress (2000) Evaluating elliptic functions and their inverses. Comput. Math. Appl. 39 (3-4), pp. 131–136.
  • P. L. Walker (1991) Infinitely differentiable generalized logarithmic and exponential functions. Math. Comp. 57 (196), pp. 723–733.
  • P. L. Walker (2012) Reduction formulae for products of theta functions. J. Res. Nat. Inst. Standards and Technology 117, pp. 297–303.
  • R. S. Ward (1987) The Nahm equations, finite-gap potentials and Lamé functions. J. Phys. A 20 (10), pp. 2679–2683.
  • G. N. Watson (1937) Two tables of partitions. Proc. London Math. Soc. (2) 42, pp. 550–556.
  • 9: Bibliography L
  • P. W. Lawrence, R. M. Corless, and D. J. Jeffrey (2012) Algorithm 917: complex double-precision evaluation of the Wright ω function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
  • D. J. Leeming (1977) An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.
  • J. Lehner (1941) A partition function connected with the modulus five. Duke Math. J. 8 (4), pp. 631–655.
  • J. Lepowsky and S. Milne (1978) Lie algebraic approaches to classical partition identities. Adv. in Math. 29 (1), pp. 15–59.
  • L. Lorch and P. Szegő (1964) Monotonicity of the differences of zeros of Bessel functions as a function of order. Proc. Amer. Math. Soc. 15 (1), pp. 91–96.
  • 10: Bibliography
  • D. E. Amos (1989) Repeated integrals and derivatives of K Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.
  • G. E. Andrews (1966a) On basic hypergeometric series, mock theta functions, and partitions. II. Quart. J. Math. Oxford Ser. (2) 17, pp. 132–143.
  • G. E. Andrews, I. P. Goulden, and D. M. Jackson (1986) Shanks’ convergence acceleration transform, Padé approximants and partitions. J. Combin. Theory Ser. A 43 (1), pp. 70–84.
  • G. E. Andrews (1976) The Theory of Partitions. Encyclopedia of Mathematics and its Applications, Vol. 2, Addison-Wesley Publishing Co., Reading, MA-London-Amsterdam.
  • G. E. Andrews (1979) Plane partitions. III. The weak Macdonald conjecture. Invent. Math. 53 (3), pp. 193–225.