Reflective Numeration Systems I: a Global Standpoint
2026-06-02 • Discrete Mathematics
Discrete Mathematics
AI summaryⓘ
The authors created a new way to extend the well-known b-ary Gray code, a special sequence of numbers, to more complex sequences called k-bonacci ones and others. They used mathematical tools that help work with lists of sequences of letters or numbers. Their method introduces the Z-Gray product, a concept that helps generate sequences avoiding certain unwanted patterns and keeps useful properties similar to the original Gray codes.
b-ary Gray codek-bonacci sequencesZ-Gray productfinite wordsfactor avoidancepower-associativityflipping digit propertysequence generationcombinatorics
Authors
Benoît Rittaud
Abstract
We present a framework to generalize the standard b-ary Gray code to get the k-bonacci ones obtained in [5] as well as many others by using theoretical tools that allow to make calculations on lists. We introduce the notion of Z-Gray product, from which we deduce sequences of lists of finite words avoiding a predefinite list Z of factors and which satisfy a power-associativity property as well a generalizations of the classical flipping digit property.