| Title:
|
Maximal upper asymptotic density of sets of integers with missing differences from a given set (English) |
| Author:
|
Pandey, Ram Krishna |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
140 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
53-69 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $M$ be a given nonempty set of positive integers and $S$ any set of nonnegative integers. Let $\overline \delta (S)$ denote the upper asymptotic density of $S$. We consider the problem of finding \[\mu (M):=\sup _{S}\overline \delta (S),\] where the supremum is taken over all sets $S$ satisfying that for each $a,b\in S$, $a-b \notin M.$ In this paper we discuss the values and bounds of $\mu (M)$ where $M = \{a,b,a+nb\}$ for all even integers and for all sufficiently large odd integers $n$ with $a<b$ and $\gcd (a,b)=1.$ (English) |
| Keyword:
|
upper asymptotic density |
| Keyword:
|
maximal density |
| MSC:
|
11B05 |
| idZBL:
|
Zbl 06433698 |
| idMR:
|
MR3324419 |
| DOI:
|
10.21136/MB.2015.144179 |
| . |
| Date available:
|
2015-03-09T17:40:37Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144179 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
