Combinatorics and Incidence Geometry

There are several categories for finite incidence structures (directed graphs, undirected graphs, incidence structures, and linear codes). The facilities for integers, sets and so on may be applied to problems in enumerative combinatorics.

• Counting
  • Partitions of a set
  • Generation of strings from a grammar
• Graphs
  • Constructors
  • Construction of Tutte's 8-cage
  • Construction of the Grötzch graph
  • Automorphism group of the 8-dimensional cube graph
• Incidence Structures and Designs
  • Automorphism group of a block design
  • Difference sets and their automorphism groups
  • Resolution of a design
• Finite Geometry
  • Hermitian unital
  • Affine plane from a projective plane by derivation
• Linear Codes
  • Minimum Weight
  • Construction of Goppa codes
  • Syndrome decoding
  • Weight distribution of a Reed-Muller code
  • Automorphism group of a Reed-Muller code

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