Preserving Log-Convexity for Generalized Pascal Triangles

Generalized Steffensen Means

On the log-convexity of combinatorial sequences

Here presented is a survey for the log-convexity of some famous combinatorial sequences. We develop techniques for dealing with the log-convexity of sequences satisfying a three-term recurrence. We also introduce the concept of q-log-convexity and establish the link with linear transformations preserving the log-convexity. MSC: 05A20; 11B73; 11B83; 11B37

Linear Transformations Preserving the Strong $q$-log-convexity of Polynomials

In this paper, we give a sufficient condition for the linear transformation preserving the strong q-log-convexity. As applications, we get some linear transformations (for instance, Morgan-Voyce transformation, binomial transformation, Narayana transformations of two kinds) preserving the strong q-log-convexity. In addition, our results not only extend some known results, but also imply the str...

Large primes in generalized Pascal triangles

In this paper, after presenting the results of the generalization of Pascal triangle (using powers of base numbers), we examine some properties of the 112-based triangle, most of all regarding to prime numbers. Additionally, an effective implementation of ECPP method is presented which enables Magma computer algebra system to prove the primality of numbers with more than 1000 decimal digits. 1 ...

Rotational and dihedral symmetries in Steinhaus and Pascal binary triangles

We give explicit formulae for obtaining the binary sequences which produce Steinhaus triangles and generalized Pascal triangles with rotational and dihedral symmetries.