Almost disjoint families of 3-term arithmetic progressions
نویسندگان
چکیده
منابع مشابه
Almost disjoint families of 3-term arithmetic progressions
We obtain upper and lower bounds for the size of a largest family of 3-term arithmetic progressions contained in [0;n 1], no two of which intersect in more than one point. Such a family consists of just under a half of all the 3-term arithmetic progressions contained in [0;n 1]. MSC: 05D99
متن کاملRainbow 3-term Arithmetic Progressions
Consider a coloring of {1, 2, . . . , n} in 3 colors, where n ≡ 0 (mod 3). If all the color classes have the same cardinality, then there is a 3-term arithmetic progression whose elements are colored in distinct colors. This rainbow variant of van der Waerden’s theorem proves the conjecture of the second author.
متن کاملOn rainbow 4-term arithmetic progressions
{sl Let $[n]={1,dots, n}$ be colored in $k$ colors. A rainbow AP$(k)$ in $[n]$ is a $k$ term arithmetic progression whose elements have different colors. Conlon, Jungi'{c} and Radoiv{c}i'{c} cite{conlon} prove that there exists an equinumerous 4-coloring of $[4n]$ which is rainbow AP(4) free, when $n$ is even. Based on their construction, we show that such a coloring of $[4n]$...
متن کاملRoth’s Theorem on 3-term Arithmetic Progressions
This article is a discussion about the proof of a classical theorem of Roth’s regarding the existence of three term arithmetic progressions in certain subsets of the integers. Before beginning with this task, however, we will take a brief look at the history and motivation behind Roth’s theorem. The questions and ideas surrounding this subject may have begun with a wonderful theorem due to van ...
متن کاملSequences Containing No 3-Term Arithmetic Progressions
A subsequence of the sequence (1, 2, ..., n) is called a 3-AP -free sequence if it does not contain any three term arithmetic progression. By r(n) we denote the length of the longest such 3-AP -free sequence. The exact values of the function r(n) were known, for n 6 27 and 41 6 n 6 43. In the present paper we determine, with a use of computer, the exact values, for all n 6 123. The value r(122)...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2005
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2004.07.010