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Reflective Numeration Systems I: a Global Standpoint
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arXiv:2606.03351v1 Announce Type: new 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...
arXiv:2606.03351v1 Announce Type: new
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.