Generalized Eulerian numbers combinatorial applications.
Generalized golden ratios of ternary alphabets
Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases in dependence...
Generalized Levinson-Durbin sequences and binomial coefficients.
Generalized near-Bell numbers.
Generalized Pascal triangles and Toeplitz matrices.
Generalized pascal triangles: overview of new results
Generalized poly-Cauchy polynomials and their interpolating functions
We give a generalization of poly-Cauchy polynomials and investigate their arithmetical and combinatorial properties. We also study the zeta functions which interpolate the generalized poly-Cauchy polynomials.
Generalized -Euler numbers and polynomials of higher order and some theoretic identities.
Generalized reciprocity laws for sums of harmonic numbers.
Generalized Rudin-Shapiro sequences
Generalized Schröder matrices arising from enumeration of lattice paths
We introduce a new family of generalized Schröder matrices from the Riordan arrays which are obtained by counting of the weighted lattice paths with steps , , , and and not going above the line . We also consider the half of the generalized Delannoy matrix which is derived from the enumeration of these lattice paths with no restrictions. Correlations between these matrices are considered. By way of illustration, we give several examples of Riordan arrays of combinatorial interest. In addition,...
Generalized Stirling numbers and polynomials.
Generalized sum-free subsets.
Generalized Vandermonde determinants
Generating functions related to partition formulæ for Fibonacci numbers.
Generating series for the Coxeter groups and applications.
Generating units modulo an odd integer by addition and subtraction
Generators for nonlinear three term recurrences involving the greatest integer function.
Generic points in the cartesian powers of the Morse dynamical system
The symbolic dynamical system associated with the Morse sequence is strictly ergodic. We describe some topological and metrical properties of the Cartesian powers of this system, and some of its other self-joinings. Among other things, we show that non generic points appear in the fourth power of the system, but not in lower powers. We exhibit various examples and counterexamples related to the property of weak disjointness of measure preserving dynamical systems.
Geometric realizations of substitutions