About the Project

combinatorial design


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1: 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)). Other areas of combinatorial analysis include graph theory, coding theory, and combinatorial designs. …
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
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
  • Combinatorial Object Server (website).

  • For algorithms for counting and analyzing combinatorial structures see Knuth (1993), Nijenhuis and Wilf (1975), and Stanton and White (1986).
    7: David M. Bressoud
    His books are Analytic and Combinatorial Generalizations of the Rogers-Ramanujan Identities, published in Memoirs of the American Mathematical Society 24, No. …
  • 8: Karl Dilcher
    Dilcher’s research interests include classical analysis, special functions, and elementary, combinatorial, and computational number theory. …
    9: Bibliography D
  • N. G. de Bruijn (1981) Pólya’s Theory of Counting. In Applied Combinatorial Mathematics, E. F. Beckenbach (Ed.), pp. 144–184.
  • D. Dumont and G. Viennot (1980) A combinatorial interpretation of the Seidel generation of Genocchi numbers. Ann. Discrete Math. 6, pp. 77–87.
  • 10: Bibliography P
  • PARI-GP (free interactive system and C library)
  • G. Pólya and R. C. Read (1987) Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds. Springer-Verlag, New York.