Monochromatic and Zero-Sum Sets of Nondecreasing Diameter
| dc.creator | Yerger, Carl R. | |
| dc.date | 2005-12-15 | |
| dc.date.accessioned | 2026-07-07T06:55:20Z | |
| dc.date.available | 2026-07-07T06:55:20Z | |
| dc.description | Let k, r, s in the natural numbers where r \geq s \geq 2. Define f(s,r,k) to be the smallest positive integer n such that for every coloring of the integers in [1,n] there exist subsets S_1 and S_2 such that: (a) S_1 and S_2 are monochromatic (but not necessarily of the same color), (b) |S_1| = s, |S_2| = r, (c)max(S_1) < min(S_2), and (d) diam(S_1) \leq diam(S_2). We prove that the theorems defining f(s,r,2) and f(s,r,3) admit a partial generalization in the sense of the Erdos-Ginzburg-Ziv theorem. This work begins the off-diagonal case of the results of Bialostocki, Erdos, and Lefmann. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0512363 | |
| dc.identifier | http://arxiv.org/abs/math/0512363 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106249 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A18; 05D05; 05D10; 11P21 | |
| dc.title | Monochromatic and Zero-Sum Sets of Nondecreasing Diameter | |
| dc.type | text |