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The numbers less than () correspond to all k-combinations of {0, 1, ..., n − 1}. The correspondence does not depend on the size n of the set that the k-combinations are taken from, so it can be interpreted as a map from N to the k-combinations taken from N; in this view the correspondence is a bijection.
2 of 5 barcode (non-interleaved) POSTNET barcode. A two-out-of-five code is a constant-weight code that provides exactly ten possible combinations of two bits, and is thus used for representing the decimal digits using five bits. [1] Each bit is assigned a weight, such that the set bits sum to the desired value, with an exception for zero.
The idea of factoring of large numbers can be applied to words, where a factor of a word is a block of consecutive symbols. [1] Thus, "cyclop" is a factor of "encyclopedia". In addition to examining sequences in themselves, another area to consider of combinatorics on words is how they can be represented visually.
Wikipedia:Shortcut table, showing all upper- and lower-case WP: shortcuts of length one, two, or three letters; Two character combinations of single-digit-single-letter (0A–9Z), single-letter-single-digit (A0–Z9), single-letter-double-digit (A00–Z99), and two-letters (AA–ZZ).
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.
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The numbers A n are known as Euler numbers, zigzag numbers, or up/down numbers. When n is even the number A n is known as a secant number , while if n is odd it is known as a tangent number . These latter names come from the study of the generating function for the sequence.
Compare box(6,7) in the triangle. 16 tiles from the game Tantrix, corresponding to the 16 necklaces with 2 red, 2 yellow and 2 green beads. In combinatorics , a k -ary necklace of length n is an equivalence class of n -character strings over an alphabet of size k , taking all rotations as equivalent.