We introduce a q-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 q-rational numbers of Morier-Genoud and Ovsienko. They are defined as ratios of generating functions for P-partitions on certain posets. We give matrix formulas for computing them, which generalize previous results in the $q=1$ case. We also show that certain properties enjoyed by the q-rationals are also satisfied by our higher versions.
No takes yet. Share an insight, caveat, or question.
Burcroff et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: