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pro vyhledávání: '"Moore, Kenneth"'
We provide a general framework to construct colorings avoiding short monochromatic arithmetic progressions in Euclidean Ramsey theory. Specifically, if $\ell_m$ denotes $m$ collinear points with consecutive points of distance one apart, we say that $
Externí odkaz:
http://arxiv.org/abs/2404.19233
Publikováno v:
Combinatorica, 2024
A conjecture of Erd\H{o}s, Graham, Montgomery, Rothschild, Spencer and Straus states that, with the exception of equilateral triangles, any two-coloring of the plane will have a monochromatic congruent copy of every three-point configuration. This co
Externí odkaz:
http://arxiv.org/abs/2402.14197
For a two-dimensional convex body, the Kovner-Besicovitch measure of symmetry is defined as the volume ratio of the largest centrally symmetric body contained inside the body to the original body. A classical result states that the Kovner-Besicovitch
Externí odkaz:
http://arxiv.org/abs/2309.12597
We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.
Comment: 8 pages, 1 figure
Comment: 8 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2304.03920
Autor:
Moore, Kenneth, Woolgar, Eric
We prove a Bakry-\'Emery generalization of a theorem of Petersen and Wilhelm, itself a generalization of a theorem of Frankel, that closed minimal hypersurfaces in a complete manifold with a suitable curvature bound must intersect. We then prove spli
Externí odkaz:
http://arxiv.org/abs/2110.06524
Autor:
Ruiz, Alejo, Edwards, Jode W., Castellano, Michael J., Gambin, Brenda L., Licht, Mark A., Moore, Kenneth J., Archontoulis, Sotirios V.
Publikováno v:
In European Journal of Agronomy August 2024 158
