Name
Abstract | ||
|---|---|---|
Given any length k≥3 and density 0<δ≤1, we introduce and study the set Sz(k,δ) consisting of all positive integers n such that every subset of {1,2,…,n} of density at least δ contains an arithmetic progression of length k. A famous theorem of Szemerédi guarantees that this set is not empty. We show that Sz(k,δ)∪{0} is a numerical semigroup and we determine it for (k,δ)=(4,1∕2) and for more than thirty pairs (3,δ) with δ>1∕5. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.dam.2018.03.023 | Discrete Applied Mathematics |
Keywords | DocType | Volume |
Arithmetic progression,van der Waerden number,Multiplicity,Frobenius number,Conductor | Journal | 263 |
ISSN | Citations | PageRank |
0166-218X | 0 | 0.34 |
References | Authors | |
0 | 5 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sukumar Das Adhikari | 1 | 23 | 6.47 |
| Luis Boza | 2 | 7 | 6.07 |
| Shalom Eliahou | 3 | 86 | 23.92 |
| M. P. Revuelta | 4 | 24 | 7.72 |
| M. I. Sanz | 5 | 8 | 3.01 |