9 papers
Some sequences and number triangles which are related to Narayana polynomials and to q-Narayana polynomials for q=-1
Johann Cigler
As is well known the Catalan numbers can be interpreted as numbers of Dyck paths. The Narayana polynomials and the q-Narayana polynomials for q=-1 can analogously be interpreted as…
Continued fractions related to Narayana polynomials
Johann Cigler
The generating functions of some sequences of Catalan numbers and Narayana polynomials have simple expansions as continued fractions of Jacobi type. We give an overview of these fa…
Symmetric Dyck paths and q-Narayana numbers
Johann Cigler
We show that the q-Narayana numbers for q=-1 count symmetric Dyck paths according to the number of their valleys.
Nice q-analogs of orthogonal polynomials with nice moments: Some simple examples
Johann Cigler
In this note I collect some typical examples of orthogonal polynomials with simple moments where both moments and orthogonal polynomials have nice q-analogs.
Some elementary remarks on the powers of a partial theta function and corresponding q-analogs of the binomial coefficients
Johann Cigler
We obtain formulas for the coefficients of positive and negative powers of a partial theta function.
Hankel determinants of backward shifts of the coefficients of a partial theta function
Johann Cigler
We study some polynomials which are related to Hankel determinants of backward shifts of the coefficients of a partial theta function. In this version an appendix is added which gi…
Some remarks about Hankel determinants which are related to Catalan-like numbers
Johann Cigler
This note presents some results about Hankel determinants of backwards shifted Catalan-like numbers and related sequences.
Hankel determinants of convolution powers of Catalan numbers revisited
Johann Cigler
Using a slightly generalized result of George Andrews and Jet Wimp this note gives a simple computational proof of some Hankel determinants of backwards shifts of convolution power…
Some results and conjectures about Hankel determinants of sequences which are related to Catalan-like numbers
Johann Cigler
Martin Aigner introduced Catalan-like numbers as elements of the first column of admissible matrices and studied Hankel determinants of their forward shifts. In this paper we colle…