episciences.org_394_20230323000459663
20230323000459663
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Discrete Mathematics & Theoretical Computer Science
13658050
01
01
2007
Vol. 9 no. 2
Addition and multiplication of betaexpansions in generalized Tribonacci base
Petr
Ambrož
Zuzana
Masáková
Edita
Pelantová
https://orcid.org/0000000338172943
We study properties of βnumeration systems, where β > 1 is the real root of the polynomial x3  mx2  x  1, m ∈ ℕ, m ≥ 1. We consider arithmetic operations on the set of βintegers, i.e., on the set of numbers whose greedy expansion in base β has no fractional part. We show that the number of fractional digits arising under addition of βintegers is at most 5 for m ≥ 3 and 6 for m = 2, whereas under multiplication it is at most 6 for all m ≥ 2. We thus generalize the results known for Tribonacci numeration system, i.e., for m = 1. We summarize the combinatorial properties of infinite words naturally defined by βintegers. We point out the differences between the structure of βintegers in cases m = 1 and m ≥ 2.
01
01
2007
394
https://hal.science/hal00966530v1
10.46298/dmtcs.394
https://dmtcs.episciences.org/394

https://dmtcs.episciences.org/394/pdf

https://dmtcs.episciences.org/394/pdf