6 citations · 23 across the 28 of their papers we have counts for
6 papers · 1 filter
Origami rings
Joe Buhler, Steve Butler, Warwick de Launey +1
Motivated by a question in origami, we consider sets of points in the complex plane constructed in the following way. Let be the line in the complex plane through with…
A construction of cospectral graphs for the normalized Laplacian
Steve Butler, Jason Grout
We give a method to construct cospectral graphs for the normalized Laplacian by a local modification in some graphs with special structure. Namely, under some simple assumptions, w…
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…