On some problems about ternary paths: a linear algebra approach

Ternary paths consist of an upstep one unit, a downstep two units, never go below the x-axis, and return to x-axis. This paper addresses enumeration partial ternary paths, ending at given level i, reading path either from left-to-right or right-to-left. Since are not symmetric with respect left vs. right, as classical Dyck this leads different results. The right-to-left is quite challenging, but end very satisfying methods elementary (solving systems linear equations). In way, several conjectures open in Naiomi Cameron’s Ph.D. thesis could be successfully settled.