- Title
- Lower bounds for periods of Ducci sequences
- Creator
- Breuer, Florian; Shparlinski, Igor E.
- Relation
- ARC.DP180100201
- Relation
- Bulletin of The Australian Mathematical Society Vol. 102, Issue 1, p. 31-38
- Publisher Link
- http://dx.doi.org/10.1017/S0004972719001187
- Publisher
- Cambridge University Press
- Resource Type
- journal article
- Date
- 2020
- Description
- A Ducci sequence is a sequence of integer n-tuples obtained by iterating the map: D:(a1,a2,…,an)↦(|a1−a2|,|a2−a3|,…,|an−a1|). Such a sequence is eventually periodic and we denote by P(n) the maximal period of such sequences for given odd n. We prove a lower bound for P(n) by counting certain partitions. We then estimate the size of these partitions via the multiplicative order of two modulo n.
- Subject
- Ducci sequence; finite field; multiplicative order; partition
- Identifier
- http://hdl.handle.net/1959.13/1439207
- Identifier
- uon:40854
- Identifier
- ISSN:0004-9727
- Language
- eng
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