About: Telephone number (mathematics)

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In mathematics, the telephone numbers or the involution numbers form a sequence of integers that count the ways n people can be connected by person-to-person telephone calls. These numbers also describe the number of matchings (the Hosoya index) of a complete graph on n vertices, the number of permutations on n elements that are involutions, the sum of absolute values of coefficients of the Hermite polynomials, the number of standard Young tableaux with n cells, and the sum of the degrees of the irreducible representations of the symmetric group. Involution numbers were first studied in 1800 by Heinrich August Rothe, who gave a recurrence equation by which they may be calculated, giving the values (starting from n = 0)

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rdfs:label	Telephone number (mathematics) (en)
rdfs:comment	In mathematics, the telephone numbers or the involution numbers form a sequence of integers that count the ways n people can be connected by person-to-person telephone calls. These numbers also describe the number of matchings (the Hosoya index) of a complete graph on n vertices, the number of permutations on n elements that are involutions, the sum of absolute values of coefficients of the Hermite polynomials, the number of standard Young tableaux with n cells, and the sum of the degrees of the irreducible representations of the symmetric group. Involution numbers were first studied in 1800 by Heinrich August Rothe, who gave a recurrence equation by which they may be calculated, giving the values (starting from n = 0) (en)
foaf:depiction
dcterms:subject	Enumerative combinatorics Factorial and binomial topics Matching (graph theory) Permutations Integer sequences
Wikipage page ID	35258497 (xsd:integer)
Wikipage revision ID	1122569833 (xsd:integer)
Link from a Wikipage to another Wikipage	Power of two Robinson–Schensted correspondence Representation theory Binomial coefficient Enumerative combinatorics Hosoya index John Riordan (mathematician) Permutation Cycle detection Integer sequence Factorial and binomial topics Matching (graph theory) Permutations Complete graph Matching (graph theory) Mathematics Chemical graph theory Chessboard Stirling's approximation Pólya enumeration theorem Matching polynomial Mathematical chess problem Heinrich August Rothe Irreducible representation Integer sequences Exponential generating function P-adic order Graph theory Recurrence relation Involution (mathematics) Taylor series Ferrers diagram Asymptotic analysis Summation Eight queens puzzle Polyomino Double factorial Recurrence equation Young tableau Symmetric group Hermite polynomial Prime factorization Combinatorial enumeration
sameAs	Telephone number (mathematics) Telephone number (mathematics) Telephone number (mathematics) Telephone number (mathematics)
dbp:wikiPageUsesTemplate	dbt:About dbt:Math dbt:Mvar dbt:OEIS dbt:Pp dbt:Reflist dbt:Short_description dbt:Chess_diagram dbt:Bi
thumbnail	wiki-commons:Special:FilePath/K4_matchings.svg?width=300
has abstract	In mathematics, the telephone numbers or the involution numbers form a sequence of integers that count the ways n people can be connected by person-to-person telephone calls. These numbers also describe the number of matchings (the Hosoya index) of a complete graph on n vertices, the number of permutations on n elements that are involutions, the sum of absolute values of coefficients of the Hermite polynomials, the number of standard Young tableaux with n cells, and the sum of the degrees of the irreducible representations of the symmetric group. Involution numbers were first studied in 1800 by Heinrich August Rothe, who gave a recurrence equation by which they may be calculated, giving the values (starting from n = 0) 1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496, ... (sequence in the OEIS). (en)
gold:hypernym	Sequence
prov:wasDerivedFrom	wikipedia-en:Telephone_number_(mathematics)?oldid=1122569833&ns=0
page length (characters) of wiki page	15893 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Telephone_number_(mathematics)
is Link from a Wikipage to another Wikipage of	Hosoya index Random permutation statistics Complete graph Matching (graph theory) 700 (number) 76 (number) Heinrich August Rothe 9000 (number) 232 (number) 26 (number)

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