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 Staircases: Recurrence and Symmetry
We study infinite translation surfaces which are -covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithüsen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.
Generalized Stirling numbers and polynomials.
Generalized sum-free subsets.
Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication
A fractional differential controller for incommensurate fractional unified chaotic system is described and proved by using the Gershgorin circle theorem in this paper. Also, based on the idea of a nonlinear observer, a new method for generalized synchronization (GS) of this system is proposed. Furthermore, the GS technique is applied in secure communication (SC), and a chaotic masking system is designed. Finally, the proposed fractional differential controller, GS and chaotic masking scheme are...
Generalized Vandermonde determinants
Generalizing a theorem of Schur
In a letter written to Landau in 1935, Schur stated that for any integer , there are primes such that . In this note, we use the Prime Number Theorem and extend Schur’s result to show that for any integers and real , there exist primes such that
Generalizing the Birch-Stephens theorem. I. Modular curves.
Generating function identities for , via the WZ method.
Generating functions and generalized Dedekind sums.
Generating functions for the digital sum and other digit counting sequences.
Generating functions of finitely generated Witt rings
Generating functions related to partition formulæ for Fibonacci numbers.
Generating linear spans over finite fields
Generating normal numbers over Gaussian integers
Generating series for the Coxeter groups and applications.
Generating units modulo an odd integer by addition and subtraction
Generation of class fields by the modular function
Generation of Hauptmoduln of Γ1(N) by Weierstrass units and application to class fields
We show that the modular functions j 1,N generate function fields of the modular curve X 1(N), N ∈ {7; 8; 9; 10; 12}, and apply them to construct ray class fields over imaginary quadratic fields.