Integer sequences | Factorial and binomial topics | Enumerative combinatorics | Matching (graph theory) | Permutations
Telephone number (mathematics)
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). (Wikipedia).
