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Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures.It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
Combinatorics on words is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages. The subject looks at letters or symbols, and the sequences they form. Combinatorics on words affects various areas of mathematical study, including algebra and computer science. There have been a ...
Combinatorics, a MathWorld article with many references. Combinatorics, from a MathPages.com portal. The Hyperbook of Combinatorics, a collection of math articles links. The Two Cultures of Mathematics by W. T. Gowers, article on problem solving vs theory building
Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria, and is in particular concerned with "counting" the objects in those collections (enumerative combinatorics) and with deciding whether certain "optimal" objects exist (extremal combinatorics).
Combinatorics has always played an important role in quantum field theory and statistical physics. [3] However, combinatorial physics only emerged as a specific field after a seminal work by Alain Connes and Dirk Kreimer , [ 4 ] showing that the renormalization of Feynman diagrams can be described by a Hopf algebra .
Combinatorial matrix theory is a branch of linear algebra and combinatorics that studies matrices in terms of the patterns of nonzeros and of positive and negative values in their coefficients. [1] [2] [3] Concepts and topics studied within combinatorial matrix theory include: (0,1)-matrix, a matrix whose coefficients are all 0 or 1
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Annals of Combinatorics is a quarterly peer-reviewed scientific journal covering research in combinatorics. It was established in 1997 [ 1 ] by William Chen [ 2 ] and is published by Birkhäuser . The journal publishes articles in combinatorics and related areas with a focus on algebraic combinatorics , analytic combinatorics , graph theory ...