Centered polygon numbers, heptagons and nonagons, and the Robbins numbers
Combinatorics
2021-04-09 v2
Abstract
In this note, we explore certain determinantal descriptions of the Robbins numbers. Techniques used for this include continued fractions, Riordan arrays and series inversion. Proven and conjectured representations involve the determinants of both Hankel and symmetric matrices. In specific cases, links are drawn to centered polygonal numbers, and to heptagons and nonagons. We conjecture a Hankel transform determinant for the Robbins numbers related to the Fibonacci and the Catalan numbers.
Keywords
Cite
@article{arxiv.2104.01644,
title = {Centered polygon numbers, heptagons and nonagons, and the Robbins numbers},
author = {Paul Barry},
journal= {arXiv preprint arXiv:2104.01644},
year = {2021}
}
Comments
46 pages. More examples added