partitions
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1: 26.19 Mathematical Applications
§26.19 Mathematical Applications
… ►Partitions and plane partitions have applications to representation theory (Bressoud (1999), Macdonald (1995), and Sagan (2001)) and to special functions (Andrews et al. (1999) and Gasper and Rahman (2004)). …2: 26.21 Tables
§26.21 Tables
►Abramowitz and Stegun (1964, Chapter 24) tabulates binomial coefficients for up to 50 and up to 25; extends Table 26.4.1 to ; tabulates Stirling numbers of the first and second kinds, and , for up to 25 and up to ; tabulates partitions and partitions into distinct parts for up to 500. ►Andrews (1976) contains tables of the number of unrestricted partitions, partitions into odd parts, partitions into parts , partitions into parts , and unrestricted plane partitions up to 100. …3: 26.9 Integer Partitions: Restricted Number and Part Size
§26.9 Integer Partitions: Restricted Number and Part Size
►§26.9(i) Definitions
… ►Unrestricted partitions are covered in §27.14. … ►§26.9(ii) Generating Functions
… ►§26.9(iii) Recurrence Relations
…4: 26.2 Basic Definitions
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Partition
… ►As an example, , , is a partition of . … ►The total number of partitions of is denoted by . …For the actual partitions () for see Table 26.4.1. ►The integers whose sum is are referred to as the parts in the partition. …5: 26.10 Integer Partitions: Other Restrictions
§26.10 Integer Partitions: Other Restrictions
►§26.10(i) Definitions
… ►§26.10(ii) Generating Functions
… ►§26.10(iv) Identities
… ►6: 26.20 Physical Applications
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►The latter reference also describes chemical applications of other combinatorial techniques.
►Applications of combinatorics, especially integer and plane partitions, to counting lattice structures and other problems of statistical mechanics, of which the Ising model is the principal example, can be found in Montroll (1964), Godsil et al. (1995), Baxter (1982), and Korepin et al. (1993).
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7: 26.12 Plane Partitions
§26.12 Plane Partitions
►§26.12(i) Definitions
… ►Different configurations are counted as different plane partitions. … ► … ►The plane partition in Figure 26.12.1 is an example of a cyclically symmetric plane partition. …8: 27.20 Methods of Computation: Other Number-Theoretic Functions
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►The recursion formulas (27.14.6) and (27.14.7) can be used to calculate the partition function for .
…To compute a particular value it is better to use the Hardy–Ramanujan–Rademacher series (27.14.9).
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