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In mathematics, a composition of an integer n is a way of writing n as the sum of a sequence of (strictly) positive integers.Two sequences that differ in the order of their terms define different compositions of their sum, while they are considered to define the same integer partition of that number.
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.
One of the earliest uses of analytic techniques for an enumeration problem came from Srinivasa Ramanujan and G. H. Hardy's work on integer partitions, [4] [5] starting in 1918, first using a Tauberian theorem and later the circle method.
3 out of 4638576 [1] or out of 580717, [2] if rotations and reflections are not counted as distinct, Hamiltonian cycles on a square grid graph 8х8. Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed.
From March 2011 to December 2012, if you bought shares in companies when Jay O. Light joined the board, and sold them when he left, you would have a -2.7 percent return on your investment, compared to a 10.1 percent return from the S&P 500.
Combinatorial designs date to antiquity, with the Lo Shu Square being an early magic square.One of the earliest datable application of combinatorial design is found in India in the book Brhat Samhita by Varahamihira, written around 587 AD, for the purpose of making perfumes using 4 substances selected from 16 different substances using a magic square.
In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes.
The main result of Kneser's 1953 article [1] is a variant of Mann's theorem on Schnirelmann density.. If is a subset of , the lower asymptotic density of is the number _ ():= | {, …,} |.