2 citations · 4 across the 5 of their papers we have counts for
6 papers
The vector graph and the chromatic number of the plane, or how NOT to prove that
Jeremy F. Alm, Jacob Manske
The chromatic number of the plane is known to be some integer between 4 and 7, inclusive. We prove a limiting result that says, roughly, that one cann…
Sum-free cyclic multi-bases and constructions of Ramsey algebras
Jeremy F. Alm, Jacob Manske
Given , is called a \emph{cyclic basis} if , \emph{symmetric} if implies , and \emph{sum-free} if $(X+X)\c…
On Radial Colorings of Annuli
Jeremy F. Alm, Jacob Manske
We consider the chromatic numbers of unit-distance graphs of various annuli. In particular, we consider radial colorings, which are "nice" colorings, and completely determine the r…
A new approach to the results of Kövari, Sós, and Turán concerning rectangle-free subsets of the grid
Jeremy F. Alm, Jacob Manske
For positive integers and , define to be the smallest integer such that any subset of the integer grid with contains a rectangle;…
Three layer -free families in the Boolean lattice
Jacob Manske, Jian Shen
We prove that the largest -free family of subsets of which contains sets of at most three different sizes has at most …
-free families in the Boolean lattice
Maria Axenovich, Jacob Manske, Ryan R. Martin
For a family of subsets of [n]=\{1, 2, ..., n} ordered by inclusion, and a partially ordered set P, we say that is P-free if it does not contain a subpo…