On some questions by Cameron about ternary paths --- a linear algebra approach
Helmut Prodinger · arXiv (Cornell University) · 2019
Ternary paths consist of an up-step of one unit, a down-step of two units, never go below the $x$-axis, and return to the $x$-axis. This paper addresses the enumeration of partial ternary paths, ending at a given level $i$, starting at the left end or starting at the right end. The latter is quite challenging, but leads at the end to very satisfying results. The methods are elementary (solving systems of linear equations). In this way, several conjectures left open in Cameron's Ph.D. thesis could be successfully settled.