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On A Property Of Minimal Zero‐Sum Sequences And Restricted Sumsets
Author(s) -
Gao Weidong,
Geroldinger Alfred
Publication year - 2005
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609305004315
Subject(s) - subsequence , mathematics , abelian group , combinatorics , zero (linguistics) , sequence (biology) , product (mathematics) , longest increasing subsequence , element (criminal law) , discrete mathematics , mathematical analysis , linguistics , philosophy , geometry , biology , political science , law , bounded function , genetics
Let G be an additively written abelian group, and let S be a sequence in G ∖ {0} with length |S| ⩾ 4. Suppose that S is a product of two subsequences, say S = BC , such that the element g + h occurs in the sequence S whenever g . h is a subsequence of B or of C . Then S contains a proper zero‐sum subsequence, apart from some well‐characterized exceptional cases. This result is closely connected with restricted set addition in abelian groups. Moreover, it solves a problem on the structure of minimal zero‐sum sequences, which recently occurred in the theory of non‐unique factorizations. 2000 Mathematics Subject Classification 11B50, 11B75, 11P99.