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- Ordered_Bell_number abstract "In number theory and enumerative combinatorics, the ordered Bell numbers or Fubini numbers count the number of weak orderings on a set of n elements (orderings of the elements into a sequence allowing ties, such as might arise as the outcome of a horse race). Starting from n = 0, these numbers are1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, 102247563, ... (sequence A000670 in OEIS).The ordered Bell numbers may be computed via a summation formula involving binomial coefficients, or by using a recurrence relation. Along with the weak orderings, they count several other types of combinatorial objects that have a bijective correspondence to the weak orderings, such as the ordered multiplicative partitions of a squarefree number or the faces of all dimensions of a permutohedron (e.g. the sum of faces of all dimensions in the truncated octahedron is 1 + 14 + 36 + 24 = 75).".
- Ordered_Bell_number thumbnail 13-Weak-Orders.svg?width=300.
- Ordered_Bell_number wikiPageID "6992164".
- Ordered_Bell_number wikiPageLength "16661".
- Ordered_Bell_number wikiPageOutDegree "51".
- Ordered_Bell_number wikiPageRevisionID "675929136".
- Ordered_Bell_number wikiPageWikiLink Baseball.
- Ordered_Bell_number wikiPageWikiLink Bell_number.
- Ordered_Bell_number wikiPageWikiLink Bijective_proof.
- Ordered_Bell_number wikiPageWikiLink Binomial_coefficient.
- Ordered_Bell_number wikiPageWikiLink Category:Enumerative_combinatorics.
- Ordered_Bell_number wikiPageWikiLink Category:Integer_sequences.
- Ordered_Bell_number wikiPageWikiLink Combination_lock.
- Ordered_Bell_number wikiPageWikiLink Election.
- Ordered_Bell_number wikiPageWikiLink Enumerative_combinatorics.
- Ordered_Bell_number wikiPageWikiLink Eric_Temple_Bell.
- Ordered_Bell_number wikiPageWikiLink Eulerian_number.
- Ordered_Bell_number wikiPageWikiLink Factorial.
- Ordered_Bell_number wikiPageWikiLink Finitary_relation.
- Ordered_Bell_number wikiPageWikiLink Fubinis_theorem.
- Ordered_Bell_number wikiPageWikiLink Generating_function.
- Ordered_Bell_number wikiPageWikiLink Guido_Fubini.
- Ordered_Bell_number wikiPageWikiLink Horse_racing.
- Ordered_Bell_number wikiPageWikiLink Identity_matrix.
- Ordered_Bell_number wikiPageWikiLink Linguistics.
- Ordered_Bell_number wikiPageWikiLink List_of_dead_heat_horse_races.
- Ordered_Bell_number wikiPageWikiLink Lowest_common_ancestor.
- Ordered_Bell_number wikiPageWikiLink Matrix_(mathematics).
- Ordered_Bell_number wikiPageWikiLink Methods_of_contour_integration.
- Ordered_Bell_number wikiPageWikiLink Modular_arithmetic.
- Ordered_Bell_number wikiPageWikiLink Multiplicative_partition.
- Ordered_Bell_number wikiPageWikiLink Natural_language.
- Ordered_Bell_number wikiPageWikiLink Number_theory.
- Ordered_Bell_number wikiPageWikiLink Optimality_theory.
- Ordered_Bell_number wikiPageWikiLink Partition_of_a_set.
- Ordered_Bell_number wikiPageWikiLink Pascals_triangle.
- Ordered_Bell_number wikiPageWikiLink Permutohedron.
- Ordered_Bell_number wikiPageWikiLink Photo_finish.
- Ordered_Bell_number wikiPageWikiLink Recurrence_relation.
- Ordered_Bell_number wikiPageWikiLink Series_(mathematics).
- Ordered_Bell_number wikiPageWikiLink Set_(mathematics).
- Ordered_Bell_number wikiPageWikiLink Square-free_integer.
- Ordered_Bell_number wikiPageWikiLink Stirling_numbers_of_the_second_kind.
- Ordered_Bell_number wikiPageWikiLink Summation.
- Ordered_Bell_number wikiPageWikiLink Tie_(draw).
- Ordered_Bell_number wikiPageWikiLink Total_order.
- Ordered_Bell_number wikiPageWikiLink Tree_(graph_theory).
- Ordered_Bell_number wikiPageWikiLink Truncated_octahedron.
- Ordered_Bell_number wikiPageWikiLink Weak_ordering.
- Ordered_Bell_number wikiPageWikiLink File:13-Weak-Orders.svg.
- Ordered_Bell_number wikiPageWikiLink File:Cayley_ordered_Bell_trees.svg.
- Ordered_Bell_number wikiPageWikiLinkText "Ordered Bell number".
- Ordered_Bell_number wikiPageWikiLinkText "ordered Bell number".
- Ordered_Bell_number wikiPageUsesTemplate Template:Classes_of_natural_numbers.
- Ordered_Bell_number wikiPageUsesTemplate Template:Harvtxt.
- Ordered_Bell_number wikiPageUsesTemplate Template:OEIS.
- Ordered_Bell_number wikiPageUsesTemplate Template:Reflist.
- Ordered_Bell_number subject Category:Enumerative_combinatorics.
- Ordered_Bell_number subject Category:Integer_sequences.
- Ordered_Bell_number type Combinatoric.
- Ordered_Bell_number type Integer.
- Ordered_Bell_number comment "In number theory and enumerative combinatorics, the ordered Bell numbers or Fubini numbers count the number of weak orderings on a set of n elements (orderings of the elements into a sequence allowing ties, such as might arise as the outcome of a horse race). Starting from n = 0, these numbers are1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, 102247563, ...".
- Ordered_Bell_number label "Ordered Bell number".
- Ordered_Bell_number sameAs Q7100706.
- Ordered_Bell_number sameAs m.0rphffc.
- Ordered_Bell_number sameAs Q7100706.
- Ordered_Bell_number wasDerivedFrom Ordered_Bell_number?oldid=675929136.
- Ordered_Bell_number depiction 13-Weak-Orders.svg.
- Ordered_Bell_number isPrimaryTopicOf Ordered_Bell_number.