Revision #622 → #1469 · back to history
addedPermutation (two meanings)def3361dedf5
addedSix permutations of {1,2,3}06a097d1b30b
addedNumber of permutations is n!33660e3aa807
addedPermutation as bijection2bfefe418441
addedPermutation (3,1,2) as function2b00f96e5920
addedSymmetric groupc211872a91f5
addedk-permutations1f1ef9495766
addedPermutation as bijectioncc95b6522e9f
addedIdentity permutation96890c9e6495
addedSymmetric group structure1b66c38c1b2b
addedComposition not commutative5c1afccb6c42
addedActive permutation3ef91f267122
addedPassive permutation89583a0cb958
addedDecomposition into disjoint cyclesdb6e585f0ab0
addedFixed point32c2ce34c8eb
addedDerangement4ecc7d6befe0
addedTranspositione5a82df01590
addedTwo-line notatione3663cea7002
addedTwo-line notation example48ce38941e65
addedOne-line notation051da8783d8b
addedCycle notation7d41e2b5def7
addedDisjoint cycles commutee8537d8fd8ba
addedInverse via reversing cyclesc9e33d40509b
addedCanonical cycle notation2a28389ba195
addedComposition (rightmost first)95f83ee6e371
addedComposition (leftmost first)ae28f5935e31
addedComposition satisfies group axioms55f62e501a65
addedk-permutation of n7175445e9501
addedNumber of k-permutations6bb7d2888c9b
addedPochhammer / falling factorial60e17a1475d3
addedk-combination4c41626dc4dd
addedRelation of combinations to permutations20b68a1e815e
addedBinomial coefficients1c6d071a5d33
addedk-tuples67dcec7e65e0
addedNumber of k-tuplesf05b52670103
addedMultiset permutation356bd595aad1
addedMultinomial count of multiset permutations1513a7b6159f
addedAnagrams of MISSISSIPPI220083dd98c7
addedk-permutation of a multisetec2254559dbf
addedGenerating function countcda65ce4b257
addedMISSISSIPPI generating function283fd11ed1e0
addedCircular permutation45ead4ccb307
addedEquivalence of circular permutationsf26e68a2b24f
addedCount of circular permutations736713df9291
addedNumber of permutations is n!6574ac1f1996
addedStirling number of the first kind745d8d5f9194
addedCycle typef69bb647c2b6
addedCount of permutations of given cycle type57a6749ed5b6
addedNumber of cycle types is partition functionb377c288111d
addedCycle index polynomiald10d1784e943
addedConjugate of a permutation07b6bee2a9e2
addedConjugacy iff same cycle type828b5fa4d0c5
addedOrder of a permutationaeccb3001b29
addedOrder is lcm of cycle lengths1bb68185bdda
addedOrder exampled672a0e32058
addedPermutation as product of transpositions9629970020a6
addedParity well-defined (even/odd)3226da4376b9
addedSign of a permutation9544da9e4592
addedSign equals determinant of matrixcb3e425617e3
addedPermutation matrixc493b4de1879
addedMatrix construction respects composition0b4fa216eed3
addedProduct of permutation matrices632ebef5ba9a
addedInverse matrix convention78d23169e0b5
addedAscents of 34521672374df97e9cc
addedAscending runc94b86e3b946
addedIncreasing subsequence78bd5fcf200e
addedRuns of 2453167e594c6980592
addedDescents and ascending runs48244a6e02fc
addedEulerian number9c28f0d9ee36
addedExceedance78f5f4224c81
addedWeak exceedancef872449ce7d7
addedExceedances equal descents6db1fd5a5e76
addedRecord (left-to-right maximum)73c31cd41cc3
addedFoata's fundamental bijection7a2024a6e30c
addedRecords equal cycles9d6907dd8a6d
addedFoata maps weak exceedances to ascents6d7a3691d844
addedInversion16b47ca86f88
addedInversions of 231549b5f8a9a012e
addedInversions equal for σ and σ⁻¹b898cc15f322
addedSorting via adjacent transpositions6bfe23a02b4b
addedMahonian number6d0e72bfe97e
addedKobayashi enumeration formula7eac56ed8ada
addedLehmer codebe1896cd78a8
addedInversion table97afb1f5d034
addedAscent criterion from Lehmer code89f3fc0f91f9
addedNext permutation example94fbfb1c52e1
addedSteinhaus–Johnson–Trotter property7446ea9dc9f5