33 results about "Telephone number" patented technology

In mathematics, the telephone numbers or the involution numbers are a sequence of integers that count the ways n telephone lines can be connected to each other, where each line can be connected to at most one other line. 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)