• In the study of permutation patterns, there has been considerable interest in enumerating specific permutation classes, especially those with relatively...
    29 KB (1,372 words) - 09:58, 26 June 2024
  • classes, enumerated by permutation length, is called a Wilf class. The study of enumerations of specific permutation classes has turned up unexpected...
    5 KB (608 words) - 09:00, 26 April 2022
  • of permutations Enumerations of specific permutation classes Factorial Falling factorial Permutation matrix Generalized permutation matrix Inversion...
    4 KB (282 words) - 11:52, 17 July 2024
  • countable. If a set is enumerable it will have an uncountable infinity of different enumerations, except in the degenerate cases of the empty set or (depending...
    11 KB (1,637 words) - 17:00, 15 April 2024
  • Thumbnail for Permutation
    a permutation of a set can mean one of two different things: an arrangement of its members in a sequence or linear order, or the act or process of changing...
    77 KB (11,519 words) - 06:37, 9 August 2024
  • the permutation induced on { 1 , 2 , … , k + 1 } {\displaystyle \{1,2,\ldots ,k+1\}} is a Baxter permutation. Enumerations of specific permutation classes...
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  • Stanley–Wilf conjecture (category Permutation patterns)
    growth rate of a permutation class. Enumerations of specific permutation classes for the growth rates of specific permutation classes. Albert, Michael...
    9 KB (1,019 words) - 09:59, 26 June 2024
  • Permanent Permutation Enumerations of specific permutation classes Josephus permutation Permutation matrix Permutation pattern Permutation (disambiguation)...
    7 KB (626 words) - 21:27, 20 August 2024
  • Wilf equivalence (redirect from Wilf class)
    Wilf classes; they are the combinatorial classes of permutation classes. The counting functions and Wilf equivalences among many specific permutation classes...
    2 KB (155 words) - 02:17, 21 June 2018
  • combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given...
    28 KB (3,792 words) - 09:12, 25 August 2024
  • power series of quotients (orbits) with respect to permutation groups, where we restrict the groups of degree n to the conjugacy classes Cl ⁡ ( S n )...
    28 KB (5,182 words) - 08:47, 7 November 2023
  • Thumbnail for Double factorial
    Double factorial (category Enumerative combinatorics)
    where k = ⁠n + 1/2⁠. The two copies of k must be adjacent; removing them from the permutation leaves a permutation in which the maximum element is k −...
    28 KB (4,281 words) - 00:34, 4 August 2024
  • Thumbnail for Map (mathematics)
    class group – Group of isotopy classes of a topological automorphism group Permutation group – Group whose operation is composition of permutations Regular...
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  • uniformly random permutation of the deck. Related to card shuffling are several other problems of counting special kinds of permutations that are also answered...
    30 KB (4,446 words) - 15:50, 4 July 2024
  • Stirling numbers of the first kind arise in the study of permutations. In particular, the Stirling numbers of the first kind count permutations according to...
    37 KB (7,201 words) - 09:10, 29 July 2024
  • verification. Within class definitions, the rand and randc modifiers signal variables that are to undergo randomization. randc specifies permutation-based randomization...
    34 KB (3,977 words) - 20:08, 26 May 2024
  • provided for making heap from a range of elements, generating lexicographically ordered permutations of a range of elements, merge sorted ranges and perform...
    24 KB (2,136 words) - 01:31, 6 April 2024
  • Thumbnail for Magic square
    Every permutation of the rows or columns preserves all row and column sums, but generally not the two diagonal sums. If the same permutation p {\displaystyle...
    281 KB (22,272 words) - 04:06, 15 August 2024
  • sample of other instances. Like an inductive generalization, an inductive prediction relies on a data set consisting of specific instances of a phenomenon...
    66 KB (8,483 words) - 22:32, 7 August 2024
  • S2CID 39361123. Ten-hwang Lai; Shu-shang Wei (April 1997). "Bipartite permutation graphs with application to the minimum buffer size problem". Discrete...
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  • Thumbnail for Principia Mathematica
    p. Pp principle of tautology ✱1.3. ⊦: q .⊃. p ∨ q. Pp principle of addition ✱1.4. ⊦: p ∨ q .⊃. q ∨ p. Pp principle of permutation ✱1.5. ⊦: p ∨ ( q ∨...
    71 KB (9,458 words) - 14:09, 22 July 2024
  • the y element of an ordered pair (x, y) Partially ordered set Complete partial order Permutation, the act of arranging all the members of a set into some...
    7 KB (942 words) - 10:41, 11 August 2024
  • (i)}.} The sum here extends over all elements σ of the symmetric group Sn; i.e. over all permutations of the numbers 1, 2, ..., n. For example, perm ⁡ (...
    27 KB (4,508 words) - 06:01, 10 May 2024
  • Thumbnail for Stirling numbers of the second kind
    variable X be the number of fixed points of a uniformly distributed random permutation of a finite set of size m. Then the nth moment of X is E ( X n ) = ∑...
    24 KB (4,043 words) - 11:39, 24 August 2024
  • Thumbnail for Census
    Census (category Wikipedia articles in need of updating from June 2024)
    be derived from census enumerations. In some countries, the census provides the official counts used to apportion the number of elected representatives...
    53 KB (6,235 words) - 17:17, 23 August 2024
  • Thumbnail for Catalan number
    Catalan number (category Enumerative combinatorics)
    Generalized Dyck Paths, Electronic Journal of Combinatorics online Dershowitz, Nachum; Zaks, Shmuel (1980), "Enumerations of ordered trees", Discrete Mathematics...
    38 KB (5,797 words) - 18:42, 20 August 2024
  • minor. A graph G is permutationally representable if it can be represented by a word of the form p1p2...pk, where pi is a permutation. On can also say that...
    30 KB (3,653 words) - 12:19, 12 August 2024
  • short descriptions of redirect targets Permutations – Mathematical version of an order changePages displaying short descriptions of redirect targets Symmetry –...
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  • if any of the variables are interchanged, one obtains the same polynomial. Formally, P is a symmetric polynomial if for any permutation σ of the subscripts...
    21 KB (3,833 words) - 01:08, 26 January 2024
  • Thumbnail for Maximal independent set
    to be a bipartite graph. The problem is however tractable on some specific classes of graphs, for instance it is tractable on cographs. The maximal independent...
    40 KB (5,451 words) - 01:02, 17 August 2024