Small sums of five roots of unity

arXiv Code and data search.c 221000.dat plot5.ggb – Geogebra notebook geo5.sh – awk one-liner to format array to input parameters to Geogebra Errata Every time I wrote I should have written . This will be corrected in the final version. The pigeonhole upper bound is perhaps better written , since it arises as , where …

The Namer-Claimer game, part 2

Discrete Mathematics, Volume 344, Issue 3, March 2021, 112256 https://doi.org/10.1016/j.disc.2020.112256 arXiv I’ve previously written about the Namer-Claimer game.  I can now prove that the length of the game is with optimal play from each side, matching the greedy lower bound.  The upper bound makes use of randomness, but in a very controlled way.  Analysing a truly …

Minimalist designs

Ben Barber, Stefan Glock, Daniela Kühn, Allan Lo, Richard Montgomery, Deryk Osthus Random Struct Alg. 2020; 57: 47– 63. https://doi.org/10.1002/rsa.20915 In Edge decompositions of graphs with high minimum degree, Daniela Kühn, Allan Lo, Deryk Osthus and I proved that the edge sets of sufficiently dense graphs satisfying necessary divisibility conditions could be partitioned into copies of …