A general lower bound on the weak Schur number. (English) Zbl 1437.11039
Garijo, Delia (ed.) et al., Discrete mathematics days 2018. Extended abstracts of the 11th “Jornadas de matemática discreta y algorítmica” (JMDA), Sevilla, Spain, June 27–29, 2018. Amsterdam: Elsevier. Electron. Notes Discrete Math. 68, 137-142 (2018).
Summary: For integers \(k\), \(n\) with \(k, n \ge 1\), the \(n\)-color weak Schur number\(W S_k(n)\) is defined as the least integer \(N\), such that for every \(n\)-coloring of the integer interval \([1, N]\), there exists a monochromatic solution \(x_1, \ldots, x_k, x_{k + 1}\) in that interval to the equation \(x_1 + x_2 + \ldots + x_k = x_{k + 1}\), with \(x_i \ne x_j\), when \(i \ne j\). We show a relationship between \(W S_k(n + 1)\) and \(W S_k(n)\) and a general lower bound on the \(W S_k(n)\) is obtained.
For the entire collection see [Zbl 1392.05001].
For the entire collection see [Zbl 1392.05001].
MSC:
| 11B75 | Other combinatorial number theory |
Software:
CBackReferences:
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