Higher -Continued Fractions
arXiv:2408.06902
Abstract
We introduce a -analog of the higher continued fractions introduced by the last three authors in a previous work (together with Gregg Musiker), which are simultaneously a generalization of the -rational numbers of Morier-Genoud and Ovsienko. They are defined as ratios of generating functions for -partitions on certain posets. We give matrix formulas for computing them, which generalize previous results in the case. We also show that certain properties enjoyed by the -rationals are also satisfied by our higher versions.
23 pages, 7 figures