I am an Assistant Professor in the Department of Mathematics at Iowa State University (ISU). Prior to coming to ISU I did a three year NSF PostDoc under the supervision of Benny Sudakov at UCLA. Before that I earned my doctorate degree in mathematics at UC San Diego under the supervision of Fan Chung where I also worked extensively with Ron Graham.
From September 2012-February 2014, I maintained the Weekly Undergraduate Math Mailing (WUM^2) at Iowa State University. The archived announcements are available online.
A news story about by mathematics of juggling class I taught in the Fall of 2013.
Jump to Teaching,
Teaching mathematics is one of the fun parts about my job. I have taught hundreds of students at four different universities.
Steven Osborne (joint student with Leslie Hogben); Ph.D. in Fall 2013.
Papers that have been submitted:
B. Sandlund, K. Staley, M. Dixon and S. Butler, Numerical Tic-Tac-Toe on the 4x4 Board.
W. Barrett, S. Butler, M. Catral, S. Fallat, H. T. Hall, L. Hogben and M. Young, The maximum nullity of a complete subdivision graph is equal to its zero forcing number.
W. Barrett, S. Butler, M. Catral, S. Fallat, H. T. Hall, L. Hogben, P. van den Driessche and M. Young, The principal rank characteristic sequence over various fields.
S. Butler, M. Catral, S. Fallat, H. T. Hall, L. Hogben, P. van den Driessche and M. Young, The enhanced principal rank characteristic sequence.
S. Butler, J. Grout and H. T. Hall, Using variants of zero forcing to bound the inertia set of a graph.
Papers that will appear:
S. Butler, R. Graham and L. Lu, Unrolling residues to avoid progressions, to appear in Mathematics Magazine.
S. Butler and F. Chung, Spectral Graph Theory, to appear in Handbook of Linear Algebra, Second Edition, CCR Press.
S. Butler, R. Graham and R. Stong, Collapsing numbers in bases 2, 3, and beyond, to appear in the proceedings of Gathering for Gardner X.
S. Butler and S. Osborne, Counting tilings by taking walks, to appear in Journal of Combinatorial Mathematics and Combinatorial Computing 88 (2014), ???-???.
S. Butler, Backwards addition, to appear in the proceedings of Gathering for Gardner X.
A. Alhakim, S. Butler and R. Graham, de Bruijn sequences with varying combs, to appear in INTEGERS: The Electronic Journal of Combinatorial Number Theory.
Papers that have appeared:
- J. Bodeen, S. Butler, T. Kim, X. Sun and S. Wang, Tiling a strip with triangles, Electronic Journal of Combinatorics 21 (2014), P1.7, 15pp.
- S. Butler, R. Graham, G. Guettler and C. Mallows, An interstice relationship for flowers with four petals, Journal of Geometry 104 (2013), 421-438.
- S. Butler and M. Young, Throttling zero forcing propagation speed, Australasian Journal of Combinatorics 57 (2013), 65-71.
- S. Butler, E. Demaine, R. Graham and T. Tachi, Constructing points through folding and intersection, International Journal of Computational Geometry & Applications 23 (2013), 49-64.
- S. Butler and R. Graham, Subdivision using angle bisectors is dense in the space of triangles, The American Mathematical Monthly 120 (2013), 622-630.
- J. Buhler, S. Butler, W. de Launey and R. Graham, Origami rings, Journal of the Australian Mathematical Society 92 (2012), 299-311.
- S. Butler and R. Graham, A note on marking lines in [k]n, Designs, Codes and Cryptography 65 (2012), 165-175.
- W. Barrett, S. Butler, H. T. Hall, J. Sinkovic, W. So, C. Starr and A. Yielding, Computing inertia sets using atoms, Linear Algebra and its Applications 436 (2012), 4489-4502.
- S. Butler and J. Grout, A construction of cospectral graphs for the normalized Laplacian, Electronic Journal of Combinatorics 18 (2011), #231, 20pp.
- J. Buhler, S. Butler, R. Graham and E. Tressler, Hypercube orientations with only two in-degrees, Journal of Combinatorial Theory, Series A 118 (2011), 1695-1702.
- S. Butler, K. Costello and R. Graham, Finding patterns avoiding many monochromatic constellations, Experimental Mathematics 19 (2010), number 4, 399-411.
- S. Butler and R. Graham, Iterated triangle partitions, Fete of Combinatorics and Computer Science, G. Katona, A. Schrijver, T. Szonyi, eds., Bolyai Society Mathematical Studies 29, Springer-Verlag, Heidelberg (2010), 23-42.
- S. Butler, F. Chung, R. Graham and M. Laczkovich, Tiling polygons with lattice triangles, Discrete & Computational Geometry 44 (2010), 896-903.
- S. Butler, R. Graham, G. Guettler and C. Mallows, Irreducible Apollonian configurations and packings, Discrete & Computational Geometry 44 (2010), 487-506.
- S. Butler, Eigenvalues of 2-edge-coverings, Linear and Multilinear Algebra 58 (2010), 413-423.
- S. Butler and R. Graham, Shuffling with ordered cards, Journal of Combinatorics 1 (2010), 121-139.
- S. Butler and R. Graham, Enumerating (multiplex) juggling sequences, Annals of Combinatorics 13 (2010), 413-424.
- S. Butler and F. Chung, Small spectral gap in the combinatorial Laplacian implies Hamiltonian, Annals of Combinatorics 13 (2010), 403-412.
- S. Butler, P. Horn and E. Tressler, Intersecting domino tilings, The Fibonacci Quarterly 48 (2010), 114-120.
- S. Butler, R. Graham and J. Mao, How to play the majority game with a liar, Discrete Mathematics 310 (6 February 2010), 622-629.
- S. Butler and P. Karasik, A note on nested sums, Journal of Integer Sequences 13 (2010), article 10.4.4, 8 pp.
- S. Butler, Cospectral graphs for both the adjacency and normalized Laplacian Matrices, Linear and Multilinear Algebra 58 (2010), 387-390.
- S. Butler, Induced-universal graphs for graphs with bounded maximum degree, Graphs and Combinatorics 25 (2009), 461-468.
- S. Butler, The lost daughters of Gergonne, Forum Geometricorum 9 (2009), 19-26.
- S. Butler, R. Graham and N. Zang, Optimal jumping patterns, Journal of Combinatorics and Number Theory 1 (2009), 1-13.
- S. Butler, M. T. Hajiaghayi, R. D. Kleinberg and T. Leighton, Hat guessing games, SIAM Journal on Discrete Mathematics 22 (2008), 592-605. Republished in SIAM Review 51 (2009), 399-413.
- S. Butler, R. Graham and N. Zang, Jumping sequences, Journal of Integer Sequences 11 (2008), 13 pp.
- S. Butler, Estimating the number of graphs containing very long induced paths, Ars Combinatoria 88 (2008), 321-332.
- AIM minimum rank-special graphs work group, Zero forcing sets and the minimum rank of graphs, Linear Algebra and its Applications 428 (2008), 1628-1648.
- M. Bousquet-Melou and S. Butler, Forest-like permutations, Annals of Combinatorics 11 (2007), 335-354.
- S. Butler, R. Graham and J. Mao, How to play the majority game with liars, AAIM 2007, Lecture Notes in Computer Science 4508, Springer-Verlag, 221-230.
- S. Butler, Interlacing for weighted graphs using the normalized Laplacian, Electronic Journal of Linear Algebra 16 (2007), 90-98.
- S. Butler, Using discrepancy to control singular values for nonnegative matrices, Linear Algebra and its Applications 419 (2006), 486-493.
- S. Butler, Relating singular values and discrepancy of weighted directed graphs, Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm (Miami, FL, 2006), 1112-1116.
- S. Butler, Tangent line transformations, The College Mathematics Journal 34 (2003), 105-106.
AIM minimum rank-special graphs work group, Wayne Barrett, Mireille Bousquet-Melou, Joe Buhler, Fan Chung, Kevin Costello, Warwick de Launey, Erik Demaine, Ron Graham, Jason Grout, Gerhard Guettler, Mohammad Hajiaghayi, H. Tracy Hall, Paul Horn, Pavel Karasik, Robert Kleinberg, Miklos Laczkovich, Tom Leighton, Colin Mallows, Jia Mao, Steven Osborne, John Sinkovic, Wasin So, Colin Starr, Richard Stong, Tomohiro Tachi, Eric Tressler, Amy Yielding, Nan Zang
Finding patterns avoiding many monochromatic constellations (slides), delivered at UCSD combinatorics seminar; UCLA combinatorics seminar; AMS 2009 Fall Western Section Meeting; AMS 2010 Spring Central Section Meeting; Colloquim at Michigan Technological University; AMS 2011 Fall Southeastern Section Meeting.
Applications and limitations for the normalized Laplacian, delivered at 2012 Joint Mathematics Meeting.
Cospectral graphs for the normalized Laplacian (slides), delivered at 2010 SIAM Conference on Discrete Mathematics, ISU Discrete Mathematics Seminar.
Hat games and hypercube orientations (slides), delivered at Discrete Mathematics Seminar at Iowa State University; Drake University; Combinatorics Seminar at UC San Diego.
Shuffling with ordered cards (slides), delivered at Combinatorics, Groups, Algorithms, and Complexity: Conference in honor of Laci Babai's 60th birthday; 2010 Western Number Theory Conference.
Iterated partitions of triangles, delivered at The 20th Canadian Conference on Computational Geometry (co-presenter with Ron Graham); The Mathematical Interests of Peter Borwein (co-presenter with Ron Graham); Drake University.
Tiling polygons with lattice triangles (slides), delivered at INTEGERS Conference 2009.
Jumping sequences (slides), delivered at UCSD combinatorics seminar; UCLA combinatorics seminar.
Induced universal graphs (slides), delivered at UCSD combinatorics seminar; SDSU REU; BYU colloquium; Sixth Czech-Slovak International Symposium; AMS 2007 Western Sectional Meeting; ISU Discrete Mathematics Seminar; MIGHTY LII.
Eigenvalues of 2-edge-coverings, delivered at CMS Winter 2007 Meeting; UCSD combinatorics seminar.
An Erdos-Ko-Rado problem on the strip (slides), delivered at GSCC 2008.
How to play the majority game with liars (slides), delivered at AAIM07.
Enumerating (multiplex) juggling sequences, delivered at Horizon of Combinatorics; UCSD combinatorics seminar.
On permutations which are 1324 and (bar 2143) avoiding, delivered at UC Berkeley combinatorics seminar; UCSD combinatorics seminar; CalTech combinatorics seminar.
Fibonacci meets Erdos-Ko-Rado (slides), delivered at ISU math club; Drake math club.
Generalizations of Apollonian circle packings, delivered at BYU Colloquium; ISU Colloquium.
Bounding inertia sets of a graph, delivered at AMS 2011 Central Sectional meeting; 2012 Cumberland Combinatorics Conference.
Last modified: 7 February 2014