'On-line recognition of hand-generated symbols', in Proceedings of Fall Joint Computer Conference, AFIPS, Vol 32, November 1969, pp 591-601 Freeman code segments for handwriting recognition, 1969 Parsing strokes into segments, multiple-stroke characters: single-stroke characters a one-stroke character can also be a component of a multiple-stroke character Stroke segmentation using enclosing rectangle, overlap User interface for two-dimensional form MinnemanMJ66 Minneman, Milton J.

D2music.mpq file. Symmetric group

In mathematics, the symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself. Since there are n! possible permutations of a set of n symbols, it follows that the order of the symmetric group Sn is n!.Although symmetric groups can be defined on infinite sets as well, this article discusses only the finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory. For the remainder of this article, 'symmetric group' will mean a symmetric group on a finite set.The symmetric group is important to diverse areas of mathematics such as Galois theory, invariant theory, the representation theory of Lie groups, and combinatorics. Cayley's theorem states that every group G is isomorphic to a subgroup of the symmetric group on G.

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