Intrinsic Affine Positionality in Ordered Regular Languages: Fixed-Width and Genealogical Rank

Let L be an infinite prefix-closed, right-prolongable regular language over a finite ordered alphabet of nonnegative integer digits. We ask when the lexicographic ranks of its fixed-width cross-sections, or more generally unit-spaced graded ranks, admit a normalized scalar positional representation VU(a1 ··· an) = ∑j=1n ajUn-j, U0 = 1. Positionality at one root propagates [ ] The post Intrinsic…