The classical Motzkin numbers (A001006 in [1]) count the numbers of Motzkin paths (and are also related to many other combinatorial objects, see Stanley [2]). Let us recall the definition of Motzkinâ€¦ (More)

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) correspondsâ€¦ (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 ofâ€¦ (More)

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, calledâ€¦ (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;Î±, Î², r) consideredâ€¦ (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 inâ€¦ (More)

A generalized bc-system associated to a Hermitian vector bundle over a Riemann surface is introduced in close analogy to the usual rank one case. Some of the geometric analogies to the well-knownâ€¦ (More)

Normally ordered forms of functions of boson operators are important in many contexts in particular concerning Quantum Field Theory and Quantum Optics. Beginning with the seminal work of Katrielâ€¦ (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 appearingâ€¦ (More)

A simple expression for the r-generalized Fibonacci numbers is given in terms of polynomial coefficients, generalizing in a straightforward way the well-known expression of the Fibonacci numbers inâ€¦ (More)