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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회보 대한수학회보 제58권 제6호
- 발행연도
- 2021.11
- 수록면
- 1,341 - 1,354 (14page)
- DOI
- 10.4134/BKMS.b200718
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초록· 키워드
오류제보하기
Let $r \geq 2$, and let $ k_i \geq 2$ for $1 \leq i \leq r$. Mixed van der Waerden's theorem states that there exists a least positive integer $w= w(k_1, k_2, k_3, \dots, k_r;r)$ such that for any $n \geq w$, every $r$-colouring of $[1,n]$ admits a $k_i$-term arithmetic progression with colour $i$ for some $i \in [1,r]$. For $k \geq 3$ and $r \geq 2$, the mixed van der Waerden number $w(k,2,2, \dots, 2;r)$ is denoted by $w_2(k;r)$. B. Landman and A. Robertson \cite{vdw5} showed that for $k < r < \frac{3}{2} (k-1)$ and $r \geq 2k+2$, the inequality $w_2(k;r) \leq r(k-1)$ holds. In this note, we establish some results on $w_2(k;r)$ for $2 \leq r \leq k$.
목차
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참고문헌 (9)
참고문헌 신청
Tanbir Ahmed / 2009 / Some new van der Waerden numbers and some van der Waerden-type numbers / Integers 9(1):65~76
T. Ahmed / 2010 / Two new van der Waerden numbers: w(2; 3, 17) and w(2; 3, 18) / Integers 10:369~377
Tanbir Ahmed / 2012 / On Computation of Exact van der Waerden Numbers / Integers 12(3):417~425
T. Ahmed / 2013 / Some more van der Waerden numbers / J. Integer Seq 16(4):9
T. Ahmed / 2014 / On the van der Waerden numbers w(2; 3, t) / Disc. Appl. Math 174:27~51
T. Ahmed / 2010 / Two new van der Waerden numbers: w(2; 3, 17) and w(2; 3, 18) / Integers 10:369~377
Tanbir Ahmed / 2012 / On Computation of Exact van der Waerden Numbers / Integers 12(3):417~425
T. Ahmed / 2013 / Some more van der Waerden numbers / J. Integer Seq 16(4):9
T. Ahmed / 2014 / On the van der Waerden numbers w(2; 3, t) / Disc. Appl. Math 174:27~51
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