q-Catalan numbers and q-Narayana polynomials,

arXiv math CO/0507225

A note on some binomial sums,

arXiv math CO/0604431

Ein paar einfache q-Analoga des binomischen Lehrsatzes,

2005, v.2.2007

Finite q-identities related to well-known theorems of Euler and Gauss,

arXiv math CO/0610546

Some results and conjectures about recurrence relations for certain sequences of binomial sums,

arXiv math CO/0611189

Simple proofs of Bressoud's and Schur's polynomial versions of the Rogers-Ramanujan identities,

arXiv math CO/0701802

q-Fibonacci polynomials and q-Catalan numbers,


q-Abel polynomials,


Some conjectures about q-Fibonacci polynomials,


Recurrence relations for powers of q-Fibonacci polynomials,


Some remarks on the paper "Hankel determinants for some common lattice paths" by R. A. Sulanke and G. Xin,


Hankel determinants of Schroeder-like numbers,


Hankel determinants of q-exponential polynomials,


Some remarks and conjectures about Hankel determinants,

v5. 2010

Problem 11493,

Amer. Math. Monthly 117(3), 2010

A simple approach to some Hankel determinants,


q-Lucas polynomials and associated Rogers-Ramanujan type identities,


q-Fibonacci polynomials and q-Genocchi numbers,


Hankel determinants of generalized q-exponential polynomials,


Some operator identities related to q-Hermite polynomials,


Fibonacci polynomials, generalized Stirling numbers, and Bernoulli, Genocchi and tangent numbers,


How to guess and prove explicit formulas for some Hankel determinants,


Some beautiful q-analogues of Fibonacci and Lucas polynomials,


Some nice Hankel determinants,

arXiv:1109.1449. The conjectures in this paper have been proved by X.-K. Chang et al., A direct method for evaluating some nice Hankel determinants
and proofs of several conjectures, Linear Algebra Appl. 438(2013), 2523-2541

A simple approach to q-Chebyshev polynomials,

v.1 (01/18/2012), v.4: arXiv:1201.4703

A simple variant of the q-binomial theorem,

v.1 (02/20/2012)

q-Chebyshev polynomials,

v.1. (05/14/2012), v.6 arXiv:1205.5383 v4

Ramanujan's q-continued fractions and Schröder-like numbers,


Hankel determinants of some polynomial sequences


Addendum to my paper "Hankel determinants of some polynomial sequences"


Recurrences for some sequences of binomial sums II: A simpler approach

(12/21/2012). v.2. arXiv:1302.4239

A special class of Hankel determinants

(02/15/2013), v.2. arXiv:1302.4235

Continuous q-Hermite polynomials: An elementary approach

(07/01/2013), arXiv:1307.0357

Some remarks on the paper "On a curious q-hypergeometric identity" by M. J. Cantero and A. Iserles

(22/08/2013), v.2. (17/09/2013)

Discrete q-Hermite polynomials: An elementary approach

(03/09/2013), v.2. arXiv:1309.2082

Some remarks about q- Chebyshev polynomials and q-Catalan numbers and related results

(07/12/2013), v.2. arXiv:1312.2767

Some notes on q-Gould polynomials


Sum of cubes: Old proofs suggest new q-analogues

(03/19/2014), v.5. (04/03/2014), arXiv:1403.6609

Some observations about super Catalan numbers, corresponding orthogonal polynomials, and their q-analogues

(09/22/2014), v.2. (10/01/2014), v.3. (10/22/2014), arXiv:1410.0131

Some results and conjectures about a class of q-polynomials with simple moments


Some elementary q-identities

(05/27/2015), v.2. (20/06/2015)

Some elementary results and conjectures about q-Newton binomials

(09/17/2015), v.3. (09/21/2015

Some remarks and conjectures about Rogers-Szegö polynomials

(10/21/2015), v.2. (11/03/2015)

Some remarks and conjectures related to lattice paths in strips along the x-axis

(07/01/2014), v.4. (01/20/2015) arXiv:1501.04750, v.8. (01/31/2016), v.9. (06/20/2016), v.10. (06/23/2016)

Elementary observations on Rogers-Szegö polynomials

(02/24/2016), v.2. (03/23/2016), v.3. (03/30/2016) arXiv:1602.07850

Some divisibility properties of q-Fibonacci numbers


Some elementary observations on Narayana polynomials and related topics

(08/15/2016), v.2 (08/25/2016), v.3 (08/26/2016), v4. (09/05/2016), v5. (09/07/2016), v.6. (11/15/2016), arXiv:1611.05252

Some elementary observations on Narayana polynomials and related topics II: q-Narayana polynomials

(11/15/2016) arXiv:1611.05256, v.2. (11/25/2016), v.3. (11/30/2016)

Hankel determinants of harmonic numbers and related topics


Some remarks on Rogers-Szegö polynomials and Losanitsch's triangle

(09/22/2017),v.2 (09/28/2017), v.3 (10/03/2017), v.4 (10/04/2017), v.5 (11/01/2017), v.6 (11/06/2017)

Catalan numbers, Hankel determinants and Fibonacci polynomials

(01/17/2018) arXiv:1801.05608

A curious class of Hankel determinants

(03/07/2018), v.2 (03/11/2018), v.3 (03/14/2018) arXiv:1803.05164, v.4 (03/28/2018),

Some Hankel determinants with nice evaluations

(05/17/2018) Workshop at Peter Paule's 60th birthday

An interesting class of Hankel determinants (with Mike Tyson)

(07/22/2018) arXiv: 1807.08330

Some observations about determinants which are connected with Catalan numbers and related topics,

(02/15/2019), arXiv:1902.10468, v.3 (03/01/2019), v.4 (03/31/2019), v.5 (05/02/2019

Some remarks on generalized Fibonacci and Lucas polynomials,


Some determinants of Hessenberg matrices,


Hankel determinants of linear combinations of moments of orthogonal polynomials, (with Christian Krattenthaler)

(03/03/2020), arXiv:2003.01676

Some remarks on the power product expansion of the q-exponential series,

(06/11/2020), arXiv: 2006.06242

Some remarks on q-Fibonacci polynomials and q-Catalan numbers