2 citations · 3 across the 5 of their papers we have counts for
6 papers · 1 filter
Zero forcing for inertia sets
Steve Butler, Jason Grout, H. Tracy Hall
Zero forcing is a combinatorial game played on a graph with a goal of turning all of the vertices of the graph black while having to use as few "unforced" moves as possible. This l…
Unrolling residues to avoid progressions
Steve Butler, Ron Graham, Linyuan Lu
We consider the problem of coloring with colors to minimize the number of monochromatic term arithmetic progressions (or -APs for short). We show how t…
Hypercube orientations with only two in-degrees
Joe Buhler, Steve Butler, Ron Graham +1
We consider the problem of orienting the edges of the -dimensional hypercube so only two different in-degrees and occur. We show that this can be done, for two specified…
Subdivision by bisectors is dense in the space of all triangles
Steve Butler, Ron Graham
Starting with any nondegenerate triangle we can use a well defined interior point of the triangle to subdivide it into six smaller triangles. We can repeat this process with each n…
The art of juggling with two balls or A proof for a modular condition of Lucas numbers
Steve Butler
In this short note we look at the problem of counting juggling patterns with one ball or two balls with a throw at every occurrence. We will do this for both traditional juggling a…
Shuffling with ordered cards
Steve Butler, Ron Graham
We consider a problem of shuffling a deck of cards with ordered labels. Namely we split the deck of N=k^tq cards (where t>=1 is maximal) into k equally sized stacks and then take t…