Компьютерная алгебра в программе Mathematica 4
Подпакет Combinatorica задает определение ряда
Пример 11.5.
Примеры работы с подпакетом функций комбинаторики
Подпакет Combinatorica задает определение ряда функций комбинаторики и теории графов. Ниже представлены имена функций комбинаторики.
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Функции перестановок и сочетаний
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Backtrack
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BinarySearch
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Binary Subsets
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DerangementQ
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Derangements
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Distinct Permutations
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EquivalenceClasses
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EquivalenceRelationQ
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Equivalences
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Eulerian
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FromCycles
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FromlnversionVector
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GrayCode
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HeapSort
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Heapify
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HideCycles
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Index
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InversePermutation
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Inversions
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InvolutionQ
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Josephus
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Ksubsets
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Lexicographic Permutations
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LexicographicSubsets
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MinimumChangePermutations
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MultiplicationTable
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NextKSubset
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Next Permutation
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NextSubset
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NthPermutation
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NthSubset
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NumberOf Derangements
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NumberOf Involutions
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NumberOf Permu tat ion sByCycles
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PermutationGroupQ
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PermutationQ
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Permute
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Polya
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RandomHeap
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RandomKSubset
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RandomPermutation
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RandomPermutationl
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RandomPermutation2
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RandomSubset
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RankPermutation
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RankSubset
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RevealCycles
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Runs
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SamenessRelation
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SelectionSort
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SignaturePermutation
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StirlingFirst
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StirlingSecond
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Strings
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Subsets
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ToCycles
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ToInversionVector
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TransitiveQ
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<<DiscreteMath`Combinatorica`
?Permute
Permute[l, p] permutes list 1 according to permutation p.
?KSubsets
KSubsets[l, k] gives all subsets of set 1 containing exactly k
elements, ordered lexicographically.
KSubsets[{l, 2, 3, 4, 5}, 2]
{{1, 2}, {1, 3), {1, 4}, {1, 5}, {2, 3), {2, 4}, {2, 5}, {3, 4}, {3, 5}, (4, 5}}
<< DiscreteMath`Combinatorica`
MinimumChangePermutations[{1,2,3}]
{{1, 2, 3}, {2, 1, 3}, {3, 1, 2}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}}
Map[RankPermutation, Permutations[{1,2,3,4}]]
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23}
InversePermutation[{4,8,5,2,1,3,7,6}]
(5, 4, 6, 1, 3, 8, 7, 2}
Polya[Table[ RotateRight[Range[8],i], {i,8}], m]
1/8 (4m+2m2 +m4 +m8)
Table[NthSubset[n,a,b,c,d], {n,0,15}]
{{}, {a}, {b}, {a, b}, {c}, {a, c}, {b, c}, {a, b, c}, {d}, (a, d}, {b, d}, {a, b, d}, {c, d}, {a, c, d}, {b, c, d}, {a, b, c, d}}
Вторая группа функций комбинаторики представлена следующими функциями.
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Функции разделения, композиции
и картин Янга
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CatalanNumber
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Compositions
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ConstructTableau
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DeleteFromTableau
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DurfeeSquare
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EncroachingListSet
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FerrersDiagram
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FirstLexicographicTableau
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. Insert IntoTableau
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LastLexicographicTableau
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Longest IncreasingSubsequence
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NextComposition
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Next Part it ion
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NextTableau
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NumberOf Compos it ions
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NumberOf Partitions
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NumberOf Tableaux
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PartitionQ
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Partitions
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RandomComposition
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RandomPartition
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RandomTableau
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TableauClasses
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TableauQ
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TableauxToPermutation
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Tableaux
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TransposePartition
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TransposeTableau
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