arXiv subjects

G. -N. Han

Publications and source records attributed to G. -N. Han.

3 recordsLinked to original sources

arXiv2020

Perfect linear complexity profile and Apwenian sequences

Sequences with {\em perfect linear complexity profile} were defined more than thirty years ago in the study of measures of randomness for binary sequences. More recently {\em apwenian sequences}, first with values $\pm 1$, then with values in $\{0, 1\}$, were introduced in the study of Hankel determinants of automatic sequences. We explain that these two families of sequences are the same up to indexing, and give consequences and questions that this implies. We hope that this will help gathering two distinct communities of researchers.

math.NT↗

arXiv2020

On some conjectures of P. Barry

We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.

math.NT↗

arXiv2020

Derivatives, Eulerian polynomials and the $g$-indexes of Young tableaux

In this paper we first present summation formulas for $k$-order Eulerian polynomials and $1/k$-Eulerian polynomials. We then present combinatorial expansions of $(c(x)D)^n$ in terms of inversion sequences as well as $k$-Young tableaux, where $c(x)$ is a differentiable function in the indeterminate $x$ and $D$ is the derivative with respect to $x$. We define the $g$-indexes of $k$-Young tableaux and Young tableaux, which have important applications in combinatorics. By establishing some relations between $k$-Young tableaux and standard Young tableaux, we express Eulerian polynomials, second-order Eulerian polynomials, André polynomials and the generating polynomials of gamma coefficients of Eulerian polynomials in terms of standard Young tableaux, which imply a deep connection among these polynomials.

math.CO↗