combinatorial design
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1: 26.19 Mathematical Applications
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►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)).
►Other areas of combinatorial analysis include graph theory, coding theory, and combinatorial designs.
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2: 26 Combinatorial Analysis
Chapter 26 Combinatorial Analysis
…3: 7.21 Physical Applications
§7.21 Physical Applications
… ►More recently, Cornu’s spiral appears in the design of highways and railroad tracks, robot trajectory planning, and computer-aided design; see Meek and Walton (1992). …4: Ira Gessel
5: 27.17 Other Applications
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►Schroeder (2006) describes many of these applications, including the design of concert hall ceilings to scatter sound into broad lateral patterns for improved acoustic quality, precise measurements of delays of radar echoes from Venus and Mercury to confirm one of the relativistic effects predicted by Einstein’s theory of general relativity, and the use of primes in creating artistic graphical designs.
6: 26.22 Software
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►For algorithms for counting and analyzing combinatorial structures see Knuth (1993), Nijenhuis and Wilf (1975), and Stanton and White (1986).
Combinatorial Object Server (website).
7: David M. Bressoud
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►His books are Analytic and Combinatorial
Generalizations of the Rogers-Ramanujan Identities, published in Memoirs of the American Mathematical Society 24, No.
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8: Karl Dilcher
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►Dilcher’s research interests include classical analysis, special functions, and elementary, combinatorial, and computational number theory.
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9: Bibliography D
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Pólya’s Theory of Counting.
In Applied Combinatorial Mathematics, E. F. Beckenbach (Ed.),
pp. 144–184.
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A combinatorial interpretation of the Seidel generation of Genocchi numbers.
Ann. Discrete Math. 6, pp. 77–87.
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