A numerical study of L-convex polyominoes and 201-avoiding ascent sequences

TL;DR

This paper analyzes the asymptotic behavior of L-convex polyominoes and 201-avoiding ascent sequences, providing new generating function insights and conjectures supported by initial coefficients.

Contribution

It derives asymptotics for L-convex polyominoes and conjectures a D-finite algebraic solution for 201-avoiding ascent sequences based on initial coefficients.

Findings

Asymptotic formulas for L-convex polyominoes coefficients

Conjectured algebraic generating function for 201-avoiding ascent sequences

Confirmed the conjecture with subsequent coefficients

Abstract

For L-convex polyominoes we give the asymptotics of the generating function coefficients, obtained by analysis of the coefficients derived from the functional equation given by Castiglione et al. \cite{CFMRR7}. For 201-avoiding ascent sequences, we conjecture the solution, obtained from the first 23 coefficients of the generating function. The solution is D-finite, indeed algebraic. The conjectured solution then correctly generates all subsequent coefficients. We also obtain the asymptotics, both from direct analysis of the coefficients, and from the conjectured solution. As well as presenting these new results, our purpose is to illustrate the methods used, so that they may be more widely applied.