Brylawski, Thomas Formerly, Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina.
Last reviewed:January 2020
- Permutations and combinations
- Generating functions
- Catalan numbers
- Stirling numbers
- Fibonacci numbers
- Asymptotic formulas
- Probabilistic method
- Ferrer's diagrams
- Möbius inversion
- Magic squares
- Pólya counting formula
- Application of Lefschetz theorem
- Properties of Arrangements
- Systems of distinct representatives
- Maximal systems
- Assignment problem
- Doubly stochastic matrices
- Upper-bound problem
- Existence and Construction
- Orthogonal Latin squares
- Block designs
- Projective planes
- Error-correcting codes
- Subdivision of square
- Pigeonhole principle
- Ramsey's theorem
- Related Primary Literature
- Additional Reading
The branch of mathematics which studies arrangements of elements (usually a finite number) into sets under certain prescribed constraints. Problems combinatorialists attempt to solve include the enumeration problem (how many such arrangements are there?), the structure problem (what are the properties of these arrangements and how efficiently can associated calculations be made?), and, when the constraints become more subtle, the existence problem (is there such an arrangement?).
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