Publications

Books   7   Graph Pebbling , chapter in Handbook of Discrete and Combinatorial Mathematics (2nd ed.), K. Rosen, J. Michaels, W. Goddard, J. Gross, J. Grossman and D. Shier, eds., CRC Press, Boca Raton, FL, (in press).
6   Connections in Discrete Mathematics: A Celebration of the Work of Ron Graham, S. Butler, J. Cooper, and G. Hurlbert, eds., Cambridge Univ. Press, Cambridge, (in preparation).
5   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.
4   Graph Pebbling , chapter in Modern Methods in Combinatorics 2nd Puntana School of Combinatorics, D. Jaume and S. Eliahou, eds., Centre International de Math\'ematiques Pures et Appliqu\`ees, 2013.
3   Linear Optimization: the Simplex Workbook , Springer, New York, 2010. [This book won the Textbook Excellence Award from the Text and Academic Authors Association in 2012.]
2   Proceedings of the Workshop on Generalizations of de Bruijn Cycles and Gray Codes, held at the Banff International Research Station, Banff, December 4--9, 2004. Special volume of Discrete Math., 309 no. 17 (2009), 5255--5508, edited by G. Hurlbert, B. Jackson, and B. Stevens.
1   Universal cycles: on beyond De Bruijn, Ph.D. Thesis, Rutgers University (1990).
     
Papers   67   On sparse graphs with low pebbling number (with A. Blasniak, A. Czygrinow, A. Fu, D. Herscovici, and J. Schmitt), in preparation.
66   Erdos-Ko-Rado in the weak Bruhat order (with S. Fishel, V. Kamat and K. Meagher), in preparation.
65   Pebbling in 3-paths (with L. Alcon and M. Gutierrez), in preparation.
64   On intersecting families of independent sets in trees (with V. Kamat), in preparation.
63   On the optimal pebbling number (with A. Czygrinow, G.Y. Katona, and L.F. Papp), in preparation.
62   Chvatal's conjecture for downsets of small rank (with E. Czabarka and V. Kamat) submitted.
61   Pebbling on graph products and other binary graph constructions (with J. Asplund and F. Kenter) submitted.
60   New injectives proof of the Erdos-Ko-Rado and Hilton-Milner theorems (with V. Kamat), submitted.
59   Pebbling in semi-2-trees (with L. Alcon and M. Gutierrez), Discrete Math., 340 no. 7 (2017), 1467--1480.
58   The weight function lemma for graph pebbling , J. Combin. Opt., 34 no. 2 (2017), 343--361.
57   The composer , unpublished (2016). [Gathering for Gardner 12, Atlanta, GA.]
56   Storming the castle (with C. Hurlbert), unpublished (2016). [Gathering for Gardner 12, Atlanta, GA.]
55   Pebbling in 2-paths (with L. Alcon and M. Gutierrez), Elec. Notes Discrete Math., 150 (2015), 145--150.
54   Gray codes and overlap cycles for restricted weight words (with V. Horan), Discrete Math. Algorithms Appl., 6 no. 4 (2014), 1450062, 12pp.
53   1-Overlap cycles for Steiner triple systems (with V. Horan), Des. Codes Cryptogr. 72 no. 3 (2014), 637--651.
52   Pebbling in split graphs (with L. Alcon and M. Gutierrez), SIAM J. Discrete Math. 28 no. 3 (2014), 1449--1466.
51   Overlap cycles for Steiner quadruple systems (with V. Horan), J. Combin. Des. 22 no. 2 (2014), 53--70.
50   s-Overlap cycles for permutations (with V. Horan), Bull. Inst. Combin. Appl. 69 (2013), 60--67.
49   Universal cycles for weak orders (with V. Horan), SIAM J. Discrete Math. 27 no. 3 (2013), 1360--1371.
48   t-Pebbling and extensions (with D. Herscovici and B. Hester), Graphs and Combin. 29 no. 4 (2013), 955--975.
47   General graph pebbling , Discrete Appl. Math. 161 (2013), 1221--1231.
46   Generalizations of Graham's pebbling conjecture (with D. Herscovici and B. Hester), Discrete Math. 312 no. 15 (2012), 2286--2293.
45   Linear optimization techniques for graph pebbling , http://arxiv.org/abs/1101.5641, (2011).
44   Optimal pebbling in products of graphs (with D. Herscovici and B. Hester), Austral. J. Combin. 50 (2011), 3--24.
43   Erdos-Ko-Rado theorems for chordal graphs and trees (with V. Kamat), J. Comb. Th. (A) 118 no. 3 (2011), 829--841.
42   Near-universal cycles for subsets exist (with D. Curtis, T. Hines and T. Moyer), SIAM J. Discrete Math. 23 no. 3 (2009), 1441--1449.
41   Pebbling graphs by their blocks (with D. Curtis, T. Hines and T. Moyer), Integers: Elec. J. Combin. Number Th. 9 (2009), #G2, 411--422.
40   Research problems on Gray codes and universal cycles Research problems on Gray codes and universal cycles (with B. Jackson and B. Stevens), Discrete Math. 309 no. 17 (2009), 5341--5348.
39   Preface to Proceedings of the Workshop on Generalizations of de Bruijn Cycles and Gray Codes (with B. Jackson and B. Stevens), Discrete Math. 309 no. 17 (2009), 5255--5258.
38   On universal cycles for multisets (with B. Johnson and J. Zahl), Discrete Math. 309 no. 17 (2009), 5321--5327.
37   Two new bijections on lattice paths (with V. Kamat), J. Combin. Math. Combin. Comput. 68 (2009), 215--223.
36   A short proof of the Birkhoff-von Neumann theorem , unpublished (2009). [Appears in Book 3.]
35   The pebbling threshold of the square of cliques (with A. Bekmetjev), Discrete Math. 308 no. 19 (2008), 4306--4314.
34   On the pebbling threshold of paths and the pebbling threshold spectrum (with A. Czygrinow), Discrete Math. 308 no. 15 (2008), 3297--3307.
33   On encodings of spanning trees , Discrete Appl. Math. 155 (2007), 2594--2600.
32   The equivalence of the auxiliary and shortcut methods for the Simplex algorithm , unpublished (2007). [Appears in Book 3.]
31   Cover pebbling hypercubes (with B. Munyan), Bull. Inst. Combin. Appl. 47 (2006), 71--76.
30   Girth, pebbling, and grid thresholds (with A. Czygrinow), SIAM J. Discrete Math. 20 no. 1 (2006), 1--10.
29   Recent progress in graph pebbling , Graph Theory Notes of New York XLIX (2005), 25--37.
28   On the number of ones in general binary Pascal triangles (with H. Harborth), J. Combin. Math. Combin. Comput. 54 (2005), 99--110.
27   An application of graph pebbling to zero-sum sequences in abelian groups (with S. Elledge), Integers: Elec. J. Combin. Number Th. 5(1) (2005), #A17. [This paper won the Best Undergraduate Research Award from the Mathematical Association of America in 2004.]
26   The cover pebbling number of graphs (with B. Crull, T. Cundiff, P. Feltman, L. Pudwell, Z. Szaniszlo, Z. Tuza), Discrete Math. 296 (2005), 15--23.
25   Pythagorean quadrilaterals (with R. Hochberg), Applications of Fibonacci numbers Vol. 9 (Flagstaff, AZ, 2002), 109--119, Kluwer Acad. Publ., Dordrecht, 2004.
24   Pebbling in dense graphs (with A. Czygrinow), Austral. J. Combin. 29 (2003), 201--208.
23   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. [This paper is included in the special volume Discrete Mathematics, Editor's Choice, Edition 2003, distinguished by the editors as among the 12 best of the 210 papers published that year.]
22   On pebbling threshold functions for graph sequences (with A. Czygrinow, N. Eaton, and P. M. Kayll), Discrete Math. 247 (2002), no.1-3, 93--105.
21   A note on graph pebbling (with A. Czygrinow, H. Kierstead, and W. T. Trotter), Graphs and Combin. 18 (2002), 219--225.
20   On the pebbling threshold spectrum , Electron. Notes Discrete Math., 10, Elsevier, Amsterdam, 2001. Comb01---Euroconference on Combinatorics, Graph Theory and Applications, 5 pp. (electronic).
19   Spanning trees of bounded degree (with A. Czygrinow, G. Fan, H. Kierstead, and W. T. Trotter), Elec. J. Comb. 8 (2001), no.1, Research Paper 33, 12 pages.
18   On graph pebbling, threshold functions, and supernormal posets (with N. Eaton), unpublished, (2000). [17th British Combinatorial Conference, University of Kent, Canterbury, UK]
17   A survey of graph pebbling , Congressus Numerantium 139 (1999), 41--64.
16   Two pebbling theorems , Congressus Numerantium 135 (1998), 55--63.
15   On higher dimensional perfect factors (with G. Isaak), Ars Combinatoria 45 (1997), 229--239.
14   Pebbling in diameter two graphs and products of paths (with T. Clarke and R. Hochberg), J. Graph Th. 25 (1997), no.2, 119--128.
13   On the existence of De Bruijn tori with 2 x 2 windows (with C. Mitchell and K. Paterson), J. Comb. Th. (A) 76 (1996), no.2, 213--230.
12   Equivalence class universal cycles for permutations (with G. Isaak), Discrete Math. 149 (1996), no.1-3, 123--129.
11   New constructions for De Bruijn tori (with G. Isaak), Des. Codes Cryptogr. 6 (1995), no.1, 47--56.
10   Multicover ucycles , Discrete Math. 137 (1995), no.1-3, 241--249.
9   A meshing technique for De Bruijn tori (with G. Isaak), Contemporary Math. 178 (1994), 153--160.
8   The dimension of interior levels of the boolean lattice (with A. Kostochka and L. Talysheva), Order 11 (1994), no.1, 29--40.
7   On universal cycles for k-subsets of an n-set , SIAM J. Discrete Math. 7 (1994), no.4, 598--604.
6   New results on dimension in the cube , unpublished (1994). [7th SIAM Conference on Discrete Mathematics, Albuquerque, NM.]
5   The antipodal layers problem , Discrete Math. 128 (1994), no.1-3, 237--245.
4   On spanning trees of certain graphs , unpublished (1993). [Colloquium, University of California, Santa Barbara, CA.]
3   On the De Bruijn torus problem (with G. Isaak), J. Comb. Th. (A) 64 (1993), no.1, 50--62.
2   On dimension in the cube , unpublished (1992). [872nd Meeting of the AMS, Special Session on Posets, Tuscaloosa, AL.]
1   A short proof that N3 is not a circle containment order, Order 5 (1988), no.3, 235--237.