Publications and Work in progress. 

John Caughman, 2011


For a summary of research interests, please refer to my curriculum vitae

[1] J. S. Caughman, IV, C. Dunn, N. Neudauer, and C. Starr. “Counting lattice chains and

Delannoy paths in higher dimensions,” Discrete Mathematics, 311 (2011), no. 16, pp. 1803-

1812.

 

[2] J. S. Caughman, IV, C. Haithcock, and J. J. P. Veerman. “A note on lattice chains and

Delannoy numbers,” Discrete Mathematics, 308 (2008), no. 12, pp. 2623-2628.

 

[3] J. S. Caughman, IV, E. J. Hart, and J. Ma. “The last subconstituent of the Hemmeter

graph,” Discrete Mathematics, 308 (2008), no. 14, pp. 3056-3036.

 

[4] H. A. Lewis and J. S. Caughman, IV. “Tips for the Job Search: Applying for Academic and

Postdoctoral Positions,” Notices of the Amer. Math. Soc., 53 (2006), no. 9, pp. 1021-1026.

 

[5] J. S. Caughman, IV and J. J. P. Veerman. “Kernels of directed graph Laplacians,” Electron.

J. Combin., 13 (2006), no. 1, Research Papers #39, 8 pp.

 

[6] J. J. P. Veerman, G. Lafferriere, J. S. Caughman, IV, and A. Williams. “Flocks and Formations,”

J. Stat. Phys. 121 (2005), no. 5-6, pp.901-936.

 

[7] G. Lafferriere, A. Williams, J. S. Caughman, IV, and J. J. P. Veerman. “Decentralized

control of vehicle formations,” Systems Control Lett. 54 (2005), no. 9, pp. 899-910.

 

[8] J. S. Caughman, IV, M. S. Maclean, and P. Terwilliger. “The Terwilliger algebra of an almost

bipartite P- and Q-polynomial association scheme,” Discrete Mathematics, 292 (2005), no.

1-3, pp. 17-44.

 

[9] J. S. Caughman, IV and N. Wolff. “The Terwilliger algebra of a distance-regular graph that

supports a spin model,”J. of Algebraic Combin., 21 (2005), no. 3, pp. 289-310.

 

[10] G. Lafferriere, J. S. Caughman, IV, and A. Williams. “Graph theoretic methods in the

stability of vehicle formations,” ACC2004, 2004.

 

[11] J. S. Caughman, IV. “Bipartite Q-polynomial distance-regular graphs,” Graphs and Com-

binatorics, Vol. 20, no. 1, pp.47-57, 2004.

 

[12] J. S. Caughman, IV and N. Wolff. “Parameter constraints for a distance-regular graph that

supports a spin model,” Proceedings of Com2MaC Workshop, Busan, Korea, pp.125-132,

2004.

 

[13] J. S. Caughman, IV. “The last subconstituent of a bipartite P- and Q-polynomial association

scheme,” European Journal of Combinatorics, Vol. 24, no. 5, pp.459-470, 2003

 

[14] J. S. Caughman, IV. “The parameters of bipartite Q-polynomial distance-regular graphs,”

Journal of Algebraic Combinatorics, Vol. 15, no. 3, pp.223-229, 2002

 

[15] J. S. Caughman, IV and B. E. Sagan. “The multiplicities of a dual-thin Q-polynomial

association scheme,” Electronic Journal of Combinatorics, Vol. 8, no. 1, Notes 4, 2001

 

[16] J. S. Caughman, IV. “Bipartite Q-polynomial quotients of antipodal distance-regular

graphs,” J. Combin. Theory Ser. B, vol.76, pp.291-296, 1999.

 

[17] J. S. Caughman, IV. “The Terwilliger algebras of bipartite P- and Q-polynomial association

schemes,” Discrete Math., vol.196, pp.65-95, 1999.

 

[18] J. S. Caughman, IV. “Spectra of bipartite P- and Q-polynomial association schemes,”

Graphs Combin., vol. 14, pp.321-343, 1998.

 

[19] J. S. Caughman, IV. “The Terwilliger algebra for bipartite P- and Q-polynomial association

schemes (extended abstract),” Group Theory and Combinatorial Mathematics (Japanese).

Surikaisekikenkyusho Kokyuroku, No. 991, pp.108-109, 1997.

 

[20] J. S. Caughman, IV. “Intersection numbers of bipartite distance-regular graphs,” Discrete

Math., vol.163, pp.235-241, 1997.

 

WORKS IN PROGRESS:

 

[1] J. S. Caughman, IV and J. Krussel. “Pyramidal one-factorizations and multicolored spanning

tree decompositions of K2n,” in preparation.

 

[2] J. S. Caughman, IV. “The classification of distance-regular graphs that support a spin

model,” in preparation.

 

[3] J. S. Caughman, IV and E. Lockwood. “On the existence of certain lowering maps in

polynomial rings,” in preparation.

 

[4] J. S. Caughman, IV, S. A. Bleiler, and E. Kummel. “Combinatorial bounds on the number

of linear extensions of the Boolean lattice,” in preparation.

 

[5] J. S. Caughman, IV. “A hypergeometric identity that resolves a nonnegativity conjecture

related to the parameters of a distance-regular graph,” in preparation.

 


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