Professor, Department of Mathematics and Applied Mathematics
Department Chair (Math)
Ph. D., Mathematics, Rutgers University (Ronald Graham, advisor)
M. A., Mathematics, State University of New York at Stony Brook (Joel Spencer, advisor)
B. S., Mathematics (Computer Science minor), Wake Forest University
National University of Argentina, San Luis
National University of Argentina, La Plata
Institute for Defense Analysis, La Jolla
Center for Mathematical Research, Barcelona
Autonomous University of Barcelona
Institute for Defense Analysis, Princeton
The Johns Hopkins University
I work in the areas of graph pebbling, universal cycles, extremal set theory, combinatorial optimization, combinatorial bijections, and general graph theory and discrete mathematics, as well as in mathematical education.
I have published roughly 60 articles, chapters, and books.
Books & Chapters:
Linear Optimization: The Simplex Workbook, Undergraduate Texts in Mathematics. Springer, New York, 2010.
Graph Pebbling, chapter in Handbook of Graph Theory (2nd ed.), Discrete Mathematics and its Applications, J. Gross, J. Yellen, and P. Zhang, eds. CRC Press, Boca Raton, 2014.
Proceedings of the Workshop on Generalizations of de Bruijn Cycles and Gray Codes (ed. with B. Jackson and B. Stevens), held at the Banff International Research Station, Banff, December 4–9, 2004, Discrete Math. 309 (2009), no. 17.
Graph Pebbling, chapter in Modern Methods in Combinatorics, 2nd Puntana School of Combinatorics, D. Jaume and S. Eliahou, eds. Centre International deMath´ematiques Pures et Appliqu´ees, (in press).
Pebbling in split graphs, (with L. Alc´on and M. Gutierrez) SIAM J. Discrete Math., to appear.
Overlap cycles for Steiner quadruple systems (with V. Horan), J. Combin. Des. 22 (2014), no. 2, 53–70.
Erd˝os-Ko-Rado theorems for chordal graphs and trees (with V. Kamat), J. Combin. Theory Ser. (A) 118 (2011), no. 3, 829–841.
Near-universal cycles for subsets exist (with D. Curtis, T. Hines and T. Moyer), SIAM J. Discrete Math. 23 (2009) no. 3, 1441–1449.
Two new bijections on lattice paths (with V. Kamat), J. Combin. Math. Combin. Comput. 68 (2009), 215–223.
The pebbling threshold of the square of cliques (with A. Bekmetjev), Discrete Math. 308, no. 19 (2008), 3406–3414.
An application of graph pebbling to zero-sum sequences in abelian groups (with S. Elledge), Integers 5 (2005), no. 1, A17, 10 pp.
Pythagorean quadruples (with R. Hochberg), Applications of Fibonacci numbers 9 (Flagstaff, AZ, 2002), 109–119, Kluwer Acad. Publ., Dortrecht, 2004.
Thresholds for families of multisets, with an application to graph pebbling (with A. Bekmetjev, G. Brightwell and A. Czygrinow), Discrete Math. 269 (2003) no. 1-3, 21–34.
A note on graph pebbling (with A. Czygrinow, H. A. Kierstead and W. T. Trotter), Graphs Combin. 18 (2002) no. 2, 219–225.
Spanning trees of bounded degree (with A. Czygrinow, G. Fan, H. A. Kierstead and W. T. Trotter), Electron. J. Combin. 8 (2001) no.1, Research Paper 33, 12 pp.
On the existence of De Bruijn tori with 2×2 windows (with C.Mitchell and K. Paterson), J. Combin. Theory Ser. A 76 (1996) no. 2, 213–230.
The dimension of interior levels of the boolean lattice (with A. Kostochka and L. Talysheva), Order 11 (1994) no. 1, 29–40.
On the De Bruijn torus problem (with G. Isaak), J. Combin. Theory Ser. A 64 (1993) no. 1, 50–62.
A short proof that N^3 is not a circle containment order, Order 5 (1988) no. 3, 235–237.
American Mathematical Society
Center for Discrete Mathematics and Theoretical Computer Science
Institute for Combinatorics and its Applications
Institute for Operations Research and Management Science
Mathematical Association of America
MAA Project Next Fellow
Society for Industrial and Applied Mathematics
Textbook and Academic Authors Association
HONORS & AWARDS
My research has been supported by the National Science Foundation, the National Security Agency, the J. William Fulbright Program, the Simons Foundation, the Mathematical Association of America, the Eisenhower Foundation, the Banff International Research Station, and Motorola.
I am a Fulbright Scholar and Arizona State University (ASU) Emeritus President’s Professor who has won the Distinguished Teaching Award from the Southwest Section of the Mathematical Association of America, the Charles Wexler Teaching Award from the ASU School of Mathematics & Statistical Sciences, the ASU Faculty Achievement Award for Student Mentoring, the Professor of the Year Runner-Up from the ASU Parents Association, the Texty Award from the Text and Academic Authors Association, and the Editor’s Choice Best Research Paper Award from the Journal of Discrete Mathematics.