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Maximal sum‐free sets of integer lattice grids
Author(s) -
Elsholtz Christian,
Rackham Laurence
Publication year - 2017
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12006
Subject(s) - integer lattice , integer (computer science) , mathematics , combinatorics , lattice (music) , discrete mathematics , computer science , physics , half integer , condensed matter physics , acoustics , programming language
We study the maximal density of a sum‐free set in the integer lattice{ 1 , … , n } d . For d = 2 , we show that this density is 3 5 , which solves an open problem of Aydinian and confirms a conjecture of Cameron. For d ⩾ 3 we give improved lower bounds on the density.
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