Publications (25)
Jumping sequences
Steve Butler, Ron Graham, Nan Zang
Juggling card sequences
Steve Butler, Fan Chung, Jay Cummings +1
Unrolling residues to avoid progressions
Steve Butler, Ron Graham, Linyuan Lu
A construction of cospectral graphs for the normalized Laplacian
Steve Butler, Jason Grout
Enumerating multiplex juggling patterns
Steve Butler, Jeongyoon Choi, Kimyung Kim +1
Shuffling with ordered cards
Steve Butler, Ron Graham
The art of juggling with two balls or A proof for a modular condition of Lucas numbers
Steve Butler
Rainbow arithmetic progressions
Steve Butler, Craig Erickson, Leslie Hogben +8
Counting prime juggling patterns
Esther Banaian, Steve Butler, Christopher Cox +3
The inverse eigenvalue problem of a graph: Multiplicities and minors
Wayne Barrett, Steve Butler, Shaun M. Fallat +5
Ordered multiplicity inverse eigenvalue problem for graphs on six vertices
John Ahn, Christine Alar, Beth Bjorkman +6
A cospectral family of graphs for the normalized Laplacian found by toggling
Steve Butler, Kristin Heysse
Hypercube orientations with only two in-degrees
Joe Buhler, Steve Butler, Ron Graham +1
Properties of a $q$-analogue of zero forcing
Steve Butler, Craig Erickson, Shaun Fallat +6
Subdivision by bisectors is dense in the space of all triangles
Steve Butler, Ron Graham
Using twins and scaling to construct cospectral graphs for the normalized Laplacian
Steve Butler
The mathematics of the flip and horseshoe shuffles
Steve Butler, Persi Diaconis, Ron Graham
Origami rings
Joe Buhler, Steve Butler, Warwick de Launey +1
A generalization of Eulerian numbers via rook placements
Esther Banaian, Steve Butler, Christopher Cox +3
Partition and sum is fast
Steve Butler, Ron Graham, Richard Stong
Graphs with at most two trees in a forest building process
Steve Butler, Misa Hamanaka, Marie Hardt
A forest building process on simple graphs
Zhanar Berikkyzy, Steve Butler, Jay Cummings +4
Zero forcing for inertia sets
Steve Butler, Jason Grout, H. Tracy Hall
Graph switching, 2-ranks, and graphical Hadamard matrices
Aida Abiad, Steve Butler, Willem H. Haemers
Enumerating (multiplex) juggling sequences
Steve Butler, Ron Graham