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...ur within a single 9-element [[permutation]].<ref>{{Cite OEIS|A088532|name=Patterns of permutations}}</ref> ...

==Permutation patterns== ...attern]]s, a combinatorial class of [[permutation class]]es, enumerated by permutation length, is called a [[Wilf class]].<ref>{{citation ...

...''r''&nbsp;=&nbsp;3 and ''s''&nbsp;=&nbsp;2, the formula tells us that any permutation of three numbers has an increasing subsequence of length three or a decreas === Permutation pattern interpretation === ...

...yle of [[knitting]] in which textures of crossing layers are achieved by [[permutation|permuting]] stitches. For example, given four stitches appearing on the nee ..., the "inner" cables sometimes split directions, forming complex branching patterns. Another effect is to have one cable "pierce" another cable, rather than ha ...

In [[substitution–permutation network]]s, confusion is provided by [[substitution box]]es.{{sfn|Liu|Rijme ...the ciphertext and the plain text. For example, diffusion ensures that any patterns in the plaintext, such as redundant bits, are not apparent in the ciphertex ...

...moved may consist of simple shapes, or they may be imprinted with colours, patterns, sections of a larger picture (like a jigsaw puzzle), numbers, or letters. ...d }}</ref> because the combinations of the 15 puzzle can be generated by [[Permutation#Definition|3-cycles]]. In fact, any <math>n \times m</math> sliding puzzle ...

...ge (blue arrows) and 120° vertex (pink and orange arrows) rotations that [[permutation|permute]] the tetrahedron through the positions. The twelve rotations form ...der the "objects" possessing symmetry to be geometric figures, images, and patterns, such as a [[wallpaper group|wallpaper pattern]]. For symmetry of physical ...

...circuits in graphic tensorial sums|doi-access = free}}</ref> 209 [[partial permutation]]s on four elements,<ref>{{Cite OEIS|A002720|name=Number of partial permuta ...ive primes}}</ref><ref>{{citation|title=The Call of the Primes: Surprising Patterns, Peculiar Puzzles, and Other Marvels of Mathematics|first=Owen|last=O'Shea| ...

...scription|Area of combinatorics that deals with the number of ways certain patterns can be formed}} ...iption. The [[twelvefold way]] provides a unified framework for counting [[permutation]]s, [[combination]]s and [[Partition of a set|partitions]]. ...

...the [[cyclic permutation|cycle]] structure of [[Enigma machine|Enigma]] [[permutation]]s. At top are the two rotor banks, one with lid open; below is the rheosta ...the [[cyclic permutation|cycle]] structure of [[Enigma machine|Enigma]] [[permutation]]s, thereby facilitating the decryption of German [[Enigma machine|Enigma]] ...

...to fractals and dynamical systems results from the fact that many fractal patterns have the symmetries of [[Fuchsian group]]s in general (see, for example [[I ...ersions]]. That is, if inv(''w'') denotes the number of inversions of the permutation ''w'' and ''S''_''n'' denotes the set of permutations of length ' ...

Any permutation of the corners is possible, including odd permutations. Seven of the corner ...to make the centre pieces distinguishable, which would make an odd centre permutation visible. ...

...|A collineation of the Fano plane corresponding to the 3-bit [[Gray code]] permutation]] ...tion]]'', ''[[automorphism]]'', or ''[[symmetry]]'' of the Fano plane is a permutation of the 7 points that preserves collinearity: that is, it carries [[incidenc ...

...atrices]]. Thus, the Costas arrays for any given ''n'' are a subset of the permutation matrices of order ''n''. ...Observe: {2,1,3,4} would describe the aforementioned array. This defines a permutation. This makes it easy to communicate the arrays for a given order of ''N''. ...

...where else. || ''a_ij'' = δ_{''n''+1−''i'',''j''} || A [[permutation matrix]]. == Specific patterns for entries == ...

A '''cyclic number''' is an [[integer]] for which [[cyclic permutation]]s of the digits are successive [[integer multiple]]s of the number. The m Multiples of these fractions exhibit cyclic permutation: ...

* [[Block (meteorology)]], large-scale patterns in the atmospheric pressure field * [[Block (permutation group theory)]] ...

...ac{(n_e + n_w)!}{(n_e + n_w - a - b)!(a + b)!}</math> i.e. the number of [[permutation]]s of <math>(n_e + n_w)</math> objects of which cards in the suit are indis ...tion of the thirteen cards in a hand over the four suits. In total 39 hand patterns are possible, but only 13 of them have an ''[[a priori probability]]'' exce ...

...s. The effort is purported to have driven Leffler insane. Manual [[random permutation]] is an onerous and time-consuming task that limited the number of Bingo ca ...ibility of multiple winning cards is unavoidable because any one of twelve patterns on every card can win the game. But not all 552 septillion cards need to be ...

...em.org/Doc/Examples/rubik.html "Analyzing Rubik's Cube with GAP"]'': the [[permutation group]] of Rubik's Cube is examined with [[GAP computer algebra system]]</r *[http://www.randelshofer.ch/rubik/pyraminx Patterns] A collection of pretty patterns for the Pyraminx ...