10.46298/dmtcs.394
https://dmtcs.episciences.org/394
Ambrož, Petr
Petr
Ambrož
Masáková, Zuzana
Zuzana
Masáková
Pelantová, Edita
Edita
Pelantová
0000-0003-3817-2943
Addition and multiplication of beta-expansions in generalized Tribonacci base
We study properties of β-numeration 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 β-integers, 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 β-integers 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 β-integers. We point out the differences between the structure of β-integers in cases m = 1 and m ≥ 2.
episciences.org
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
2015-06-09
2007-01-01
2007-01-01
en
journal article
https://hal.science/hal-00966530v1
1365-8050
https://dmtcs.episciences.org/394/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
Vol. 9 no. 2
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