|
Closure with a twist is a property of subsets of an algebraic structure. A subset of an algebraic structure is said to exhibit closure with a twist if for every two elements : there exists an automorphism of and an element such that : where "" is notation for an operation on preserved by . Two examples of algebraic structures with the property of closure with a twist are the cwatset and the GC-set. ==Cwatset== In mathematics, a cwatset is a set of bitstrings, all of the same length, which is closed with a twist. If each string in a cwatset, ''C'', say, is of length ''n'', then ''C'' will be a subset of Z2''n''. Thus, two strings in ''C'' are added by adding the bits in the strings modulo 2 (that is, addition without carry, or exclusive disjunction). The symmetric group on ''n'' letters, Sym(''n''), acts on Z2''n'' by bit permutation: :::''p''((''c''1,...,''c''n))=(''c''''p''(1),...,''c''''p''(n)), where ''c''=(''c''1,...,''c''n) is an element of Z2''n'' and ''p'' is an element of Sym(''n''). Closure ''with a twist'' now means that for each element ''c'' in ''C'', there exists some permutation ''p''''c'' such that, when you add ''c'' to an arbitrary element ''e'' in the cwatset and then apply the permutation, the result will also be an element of ''C''. That is, denoting addition without carry by +, ''C'' will be a cwatset if and only if ::: This condition can also be written as ::: 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Closure with a twist」の詳細全文を読む スポンサード リンク
|