Publications and Work in
progress.
John Caughman, 2011
[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,
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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