38 citations · 41 across the 5 of their papers we have counts for
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The Saturation Number of Induced Subposets of the Boolean Lattice
Michael Ferrara, Bill Kay, Lucas Kramer +4
Given a poset , a family of elements in the Boolean lattice is said to be -saturated if (1) contains no copy of as a subposet and (2) every proper superset of …
Color-blind index in graphs of very low degree
Jennifer Diemunsch, Nathan Graber, Lucas Kramer +6
Let be an edge-coloring of a graph , not necessarily proper. For each vertex , let , where is the number of edges incident…
An improved bound on the diamond-free poset problem
Lucas Kramer, Ryan R. Martin
In the theory of partially-ordered sets, the two-dimensional Boolean lattice is known as the diamond. In this paper, we show that, if is a family in the -dimension…
Rainbow arithmetic progressions
Steve Butler, Craig Erickson, Leslie Hogben +8
In this paper, we investigate the anti-Ramsey (more precisely, anti-van der Waerden) properties of arithmetic progressions. For positive integers and , the expression $aw([n…
On diamond-free subposets of the Boolean lattice
Lucas Kramer, Ryan R. Martin, Michael Young
The Boolean lattice of dimension two, also known as the diamond, consists of four distinct elements with the following property: . A diamond-free family in t…