Lower bounds for periods of Ducci sequences

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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