Matthias Schork

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A new family of generalized Stirling and Bell numbers is introduced by considering powers (V U) n of the noncommuting variables U, V satisfying U V = V U + hV s. The case s = 0 (and h = 1) corresponds to the conventional Stirling numbers of second kind and Bell numbers. For these generalized Stirling numbers, the recursion relation is given and explicit(More)
The generalized Stirling numbers S s;h (n, k) introduced recently by the authors are shown to be a special case of the three parameter family of generalized Stirling numbers S(n, k; α, β, r) considered by Hsu and Shiue. From this relation, several properties of S s;h (n, k) and the associated Bell numbers B s;h (n) and Bell polynomials B s;h|n (x) are(More)
Recently the vertex Padmakar–Ivan (PI v) index of a graph G was introduced as the sum over all edges e = uv of G of the number of vertices which are not equidistant to the vertices u and v. In this paper the vertex PI index and Szeged index of bridge graphs are determined. Using these formulas, the vertex PI indices and Szeged indices of several graphs are(More)
The generalized Stirling numbers introduced recently [11, 12] are considered in detail for the particular case s = 2 corresponding to the meromorphic Weyl algebra. A combinatorial interpretation in terms of perfect matchings is given for these meromorphic Stirling numbers and the connection to Bessel functions is discussed. Furthermore, two related(More)
It is shown that the determinants of the correlation functions of the generalized bc-system introduced recently are given as pullbacks of the non-abelian theta divisor. The usual bc-system appearing in bosonic string theory 1;2 is very well understood 1?4 and has also been considered in a rigorous algebro-geometric way by Raina 5;6. Assuming some natural(More)