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On sets of integers not containing arithmetic progressions of prescribed length
| Content Provider | Scilit |
|---|---|
| Author | Abbott, H. L. Liu, A. C. Riddell, J. |
| Copyright Year | 1974 |
| Description | Let m, n and l be positive integers satisfying m ≦ n ≦ l ≦ 3. Denote by h(m, n, l) the largest integer with the property that from every n-subset of {1,2, …, m} one can select h(m, n, l) integers no l of which are in arithmetic progression. Let f(n, l) = h(n, n, l) and let g(n, l) = $min_{m}$h(m, n, l). In what follows, by a $P_{1}$-free set we shall mean a set of integers not containing an arithmetic progression of length l. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B58F7C4E18D7772E3A21A7667E017689/S144678870001990Xa.pdf/div-class-title-on-sets-of-integers-not-containing-arithmetic-progressions-of-prescribed-length-div.pdf |
| Ending Page | 193 |
| Page Count | 6 |
| Starting Page | 188 |
| ISSN | 00049735 |
| DOI | 10.1017/s144678870001990x |
| Journal | Journal of the Australian Mathematical Society |
| Issue Number | 2 |
| Volume Number | 18 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1974-09-01 |
| Access Restriction | Open |
| Subject Keyword | Journal of the Australian Mathematical Society Integers Not Containing Sets of Integers Prescribed Length Progressions of Prescribed Containing Arithmetic Progressions |
| Content Type | Text |
| Resource Type | Article |
