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- Matthias Schork
- 2007

It is proposed that finding the recursion relation and generating function for the (colored) Motzkin numbers of higher rank introduced recently is an interesting problem.

- Toufik Mansour, Matthias Schork, Mark Shattuck
- Electr. J. Comb.
- 2011

A new family of generalized Stirling and Bell numbers is introduced by considering powers (V U)n of the noncommuting variables U, V satisfying UV = 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)

- Toufik Mansour, Matthias Schork
- Discrete Applied Mathematics
- 2009

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)

- MATTHIAS SCHORK
- 2007

Curado and Rego-Monteiro introduced in [2] a new algebraic structure generalizing the Heisenberg algebra and containing also the q-deformed oscillator as a particular case. This algebra, called generalized Heisenberg algebra, depends on an analytical function f and the eigenvalues αn of the Hamiltonian are given by the one-step recurrence αn+1 = f(αn). This… (More)

In theoretical chemistry molecular structure descriptors also called topological indices are used to understand physico-chemical properties of chemical compounds. By now there do exist a lot of different types of such indices which capture different aspects of the molecular graphs associated to the molecules considered. Arguably the most famous such index… (More)

The generalized Stirling numbers Ss;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 Ss;h(n, k) and the associated Bell numbers Bs;h(n) and Bell polynomials Bs;h|n(x) are derived. The… (More)

In this article combinatorial aspects of normal ordering annihilation and creation operators of a multi-mode boson system are discussed. The modes are assumed to be coupled since otherwise the problem of normal ordering is reduced to the corresponding problem of the single-mode case. To describe the normal ordering in the multi-mode case for each mode a… (More)

In this Letter we define generalizations of boson normal ordering. These are based on the number of contractions whose vertices are next to each other in the linear representation of the boson operator function. Our main motivation is to shed further light onto the combinatorics arising from algebraic and Fock space properties of boson operators. © 2006… (More)

- Toufik Mansour, Matthias Schork, Mark Shattuck
- Appl. Math. Lett.
- 2012

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)

- Matthias Schork
- 2001

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)