A note on the mixed van der Waerden number
Let r >= 2, and let k(i) >= 2 for 1 <= i <= r. Mixed van der Waerden's theorem states that there exists a least positive integer w = w(k(1), k(2), k(3), ..., k(r); r) such that for any n >= w, every r-colouring of 1, n] admits a k(i)-term arithmetic progression with colour i for...
保存先:
| 主要な著者: | , , |
|---|---|
| フォーマット: | 論文 |
| 出版事項: |
Korean Mathematical Society
2021
|
| 主題: | |
| オンライン･アクセス: | http://eprints.um.edu.my/27156/ |
| タグ: |
タグ追加
タグなし, このレコードへの初めてのタグを付けませんか!
|
| id |
my.um.eprints.27156 |
|---|---|
| record_format |
eprints |
| spelling |
my.um.eprints.271562022-05-25T07:33:06Z http://eprints.um.edu.my/27156/ A note on the mixed van der Waerden number Sim, Kai An Tan, Ta Sheng Wong, Kok Bin QA Mathematics Let r >= 2, and let k(i) >= 2 for 1 <= i <= r. Mixed van der Waerden's theorem states that there exists a least positive integer w = w(k(1), k(2), k(3), ..., k(r); r) such that for any n >= w, every r-colouring of 1, n] admits a k(i)-term arithmetic progression with colour i for some i is an element of 1, r]. For k >= 3 and r >= 2, the mixed van der Waerden number w(k, 2, 2, ..., 2; r) is denoted by w(2)(k; r). B. Landman and A. Robertson 9] showed that for k < r < 3/2 (k - 1) and r >= 2k + 2, the inequality w(2)(k; r) <= r(k - 1) holds. In this note, we establish some results on w(2)(k; r) for 2 <= r <= k. Korean Mathematical Society 2021 Article PeerReviewed Sim, Kai An and Tan, Ta Sheng and Wong, Kok Bin (2021) A note on the mixed van der Waerden number. Bulletin of the Korean Mathematical Society, 58 (6). pp. 1341-1354. ISSN 1015-8634, DOI https://doi.org/10.4134/BKMS.b200718 <https://doi.org/10.4134/BKMS.b200718>. 10.4134/BKMS.b200718 |
| institution |
Universiti Malaya |
| building |
UM Library |
| collection |
Institutional Repository |
| continent |
Asia |
| country |
Malaysia |
| content_provider |
Universiti Malaya |
| content_source |
UM Research Repository |
| url_provider |
http://eprints.um.edu.my/ |
| topic |
QA Mathematics |
| spellingShingle |
QA Mathematics Sim, Kai An Tan, Ta Sheng Wong, Kok Bin A note on the mixed van der Waerden number |
| description |
Let r >= 2, and let k(i) >= 2 for 1 <= i <= r. Mixed van der Waerden's theorem states that there exists a least positive integer w = w(k(1), k(2), k(3), ..., k(r); r) such that for any n >= w, every r-colouring of 1, n] admits a k(i)-term arithmetic progression with colour i for some i is an element of 1, r]. For k >= 3 and r >= 2, the mixed van der Waerden number w(k, 2, 2, ..., 2; r) is denoted by w(2)(k; r). B. Landman and A. Robertson 9] showed that for k < r < 3/2 (k - 1) and r >= 2k + 2, the inequality w(2)(k; r) <= r(k - 1) holds. In this note, we establish some results on w(2)(k; r) for 2 <= r <= k. |
| format |
Article |
| author |
Sim, Kai An Tan, Ta Sheng Wong, Kok Bin |
| author_facet |
Sim, Kai An Tan, Ta Sheng Wong, Kok Bin |
| author_sort |
Sim, Kai An |
| title |
A note on the mixed van der Waerden number |
| title_short |
A note on the mixed van der Waerden number |
| title_full |
A note on the mixed van der Waerden number |
| title_fullStr |
A note on the mixed van der Waerden number |
| title_full_unstemmed |
A note on the mixed van der Waerden number |
| title_sort |
note on the mixed van der waerden number |
| publisher |
Korean Mathematical Society |
| publishDate |
2021 |
| url |
http://eprints.um.edu.my/27156/ |
| _version_ |
1735409506483961856 |
| score |
13.251813 |