Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 31.3.2006 |
| Speaker: | Julien Bernat, IML, l'Université de la Méditerranée, France |
| Title: | Symmetrized beta-integers |
| Abstract: | Born in the late 50's, the beta-numeration allows a generalization of the notions of integers in non-integral bases called beta-integers. The set of non-negative beta-integers may be defined in various frameworks, which arise from a combinatoric, an arithmetic or a geometric point of view. However, these definitions do not match any longer for negative elements.
Under strong hypothesis on the base of numeration, we introduce a set of "symmetrized beta-integers", which unifies the above points of views. Then, we study several properties of the associated discrete structure, which are connected to topological and geometric properties of the central tile of the numeration system. |
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