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- ...s of elements. There is a set of ''n'' elements, and there are m different permutations on this set. The general research question is: can we color each element in ...e elements such that the maximum discrepancy of an interval in each of the permutations is as small as possible. ...5 KB (771 words) - 06:03, 25 September 2024
- ...'''direct sum''' of [[permutations]] are two operations to combine shorter permutations into longer ones. Given a permutation ''π'' of length ''m'' and the permut The skew sum of the permutations ''π'' = 2413 and ''σ'' = 35142 is 796835142 (the last five entries are equa ...5 KB (733 words) - 10:38, 24 September 2023
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- ...at is, the two statistics are equidistributed. For example, the number of permutations of length 4 with given major index and number of inversions is given in the ...derivation therefrom of functions of a single variable associated with the permutations of any assemblage of objects ...2 KB (327 words) - 18:06, 28 May 2023
- ...'''direct sum''' of [[permutations]] are two operations to combine shorter permutations into longer ones. Given a permutation ''π'' of length ''m'' and the permut The skew sum of the permutations ''π'' = 2413 and ''σ'' = 35142 is 796835142 (the last five entries are equa ...5 KB (733 words) - 10:38, 24 September 2023
- ...t is the [[Skew and direct sums of permutations|direct sum]] of decreasing permutations.{{r|aepv}} ...a|1999}}, which established the [[Stanley–Wilf conjecture]] for classes of permutations forbidding a layered permutation, before the conjecture was proven more gen ...5 KB (617 words) - 05:02, 1 July 2024
- ...own as a '''pattern class''', '''closed class''', or simply '''class''' of permutations. Every permutation class can be defined by the minimal permutations which do not lie inside it, its ''basis''.<ref>{{harvtxt|Kitaev|2011}}, Def ...3 KB (505 words) - 10:51, 26 June 2024
- | title = An Erdős-Ko-Rado theorem for partial permutations | title = Pattern avoidance in partial permutations ...5 KB (663 words) - 17:57, 6 November 2024
- ...s of elements. There is a set of ''n'' elements, and there are m different permutations on this set. The general research question is: can we color each element in ...e elements such that the maximum discrepancy of an interval in each of the permutations is as small as possible. ...5 KB (771 words) - 06:03, 25 September 2024
- The two smallest permutations that cannot be partitioned into an increasing and a decreasing sequence are ...to the ascending subsequence). The two forbidden patterns for skew-merged permutations, 3412 and 2143, correspond to two of the three forbidden [[induced subgraph ...5 KB (569 words) - 04:39, 1 July 2024
- {{short description|Theorem about permutations that preserve convergence for all converging series}} ...sum.<ref>{{cite journal |first=Ralph Palmer |last=Agnew |date=1955 |title=Permutations preserving convergence of series |url=https://www.ams.org/journals/proc/195 ...6 KB (912 words) - 20:54, 21 December 2024
- ...ath>2</math> and the correspondence between its vertices and the bracketed permutations of three terms <math>a</math>, <math>b</math>, and <math>c</math>.|thumb]] ...rms <math>a</math>, <math>b</math>, and <math>c</math>. There are six such permutations, <math>abc</math>, <math>acb</math>, <math>bac</math>, <math>bca</math>, <m ...5 KB (668 words) - 18:55, 15 October 2024
- ==Gilbreath permutations== ..., in terms of [[permutation pattern]]s, the Gilbreath permutations are the permutations that avoid the two patterns 132 and 312.<ref name="v">{{citation ...6 KB (977 words) - 18:06, 17 December 2024
- These permutations were introduced by [[Glen E. Baxter]] in the context of [[mathematical anal For <math>n = 1, 2, 3, \ldots</math>, the number <math>a_n</math> of Baxter permutations of length <math>n</math> is ...7 KB (913 words) - 16:49, 17 February 2025
- {{Short description|Function that is invariant under all permutations of its variables}} {{About|functions that are invariant under all permutations of their variables|the generalization of symmetric polynomials to infinitel ...5 KB (762 words) - 02:02, 18 December 2023
- {{Short description|Method of generating all permutations of n objects}} [[File:Heap algorithm with 4 elements.svg|thumb|90px|A map of the 24 permutations and the 23 swaps used in Heap's algorithm permuting the four letters A (amb ...14 KB (2,147 words) - 14:59, 6 January 2025
- ...ar = 1986}}</ref> The permutations with 1 rising sequence are the identity permutations. Instead, the number of distinct riffle shuffle permutations of a deck of <math>n</math> cards, for <math>n=1,2,3,\dots</math>, is ...7 KB (1,031 words) - 16:38, 30 July 2022
- ...nd side have positive sign for even permutations and negative sign for odd permutations of <math>x,y,z</math>. ...2 KB (344 words) - 03:02, 13 May 2024
- ...e action of the row permutations, the subgroup of ''S''<sub>''n''</sub> of permutations that permute the positions in each row separately (this "[[Young subgroup]] ...> of column permutations (another Young subgroup, defined similarly to row permutations but permuting positions within individual columns only). Then, writing the ...6 KB (933 words) - 10:29, 15 September 2024
- ==Permutations== ...ped into two positions, giving a theoretical maximum of 30!×2<sup>30</sup> permutations. This value is not reached for the following reasons: ...4 KB (574 words) - 00:04, 29 November 2024
- ...nificance by comparing the actual F test result to that gained from random permutations of the objects between the groups. Moreover, whilst PERMANOVA tests for sim ...edure draws significance for the actual F statistic by performing multiple permutations of the data. In each permutation <math>\pi</math> the items are shuffled be ...4 KB (588 words) - 18:00, 23 September 2024
- ...e)|stack data structure]]. The stack-sortable permutations are exactly the permutations that do not contain the [[permutation pattern]] 231; they are counted by th ...the permutations that this algorithm correctly sorts as being exactly the permutations that do not contain the [[permutation pattern]] 231: three elements ''x'', ...12 KB (1,593 words) - 00:52, 8 November 2023
- ...umber of ''clockwise'' rotations of corner pieces is divisible by 3; other permutations are only possible when the total number of ''clockwise'' rotations is equiv ...5 KB (843 words) - 19:04, 17 May 2024