| PUBLICATIONS: |
| [1] |
J. Caughman and T. Terada. “Proof of the Kresch-Tamvakis conjecture,” Proc. Amer. Math. Soc., 152 (2024), no. 3, pp. 1265-1277.
doi.org/10.1090/proc/16678. link,
preprint
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| [2] |
J. Caughman, A. Herman, and T. Terada. “The odd girth of generalized Johnson graphs,” Discrete Mathematics, 347 (2024), no. 7, #113985.
doi.org/10.1016/j.disc.2024.113985. link,
preprint
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| [3] |
E. Lockwood and J. Caughman. “Directions for research on proof production in combinatorics and graph theory,”
In: New Directions in University Proving: Honoring the Legacy of John and Annie Selden. (2024), To Appear. |
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| [4] |
Z.K. Reed, E. Lockwood, & J. Caughman. “From an inclination to subtract to a need to divide: exploring student understanding
and use of division in combinatorics,” 31st Annual Conference on Research in Undergraduate Mathematics Education, Omaha, NE.
(2024), To Appear. |
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| [5] |
J. Caughman, C. Dunn, J. Laison, N. Neudauer, and C. Starr. “Area, perimeter, height, and width of rectangle visibility graphs,” Journal
of Combinatorial Optimization, 46 (2023), #18, pp.1-22.
doi.org/10.1007/s10878-023-01084-9. link,
preprint
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| [6] |
A. Herman and J. Caughman. “Probability axioms and set theory paradoxes,” Symmetry, 13 (2021), no. 2, #179.
doi.org/10.3390/sym13020179. link |
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| [7] |
E. Lockwood, J. Caughman, and K. Weber. “An essay on proof, conviction and explanation: multiple representation
systems in combinatorics,” Ed. Studies in Mathematics, 103 (2020), pp.173-189.
link |
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| [8] |
P. Banda, J. Caughman, M. Cenek, and C. Teuscher. “Shift-symmetric configurations in two-dimensional
cellular automata: irreversibility, insolvability, and enumeration,” Chaos, 29 (2019), no. 6, pp.1-19.
link |
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| [9] |
E. Lockwood, J. Caughman, and K. Weber. “Multiple semantic representation systems in binomial identities:
An exploration of proofs that explain and proofs that only convince,”
22nd Annual Conference on Research in Undergraduate Mathematics Education, Oklahoma City, OK: Oklahoma State University,
(2019), pp. 37-43.
link |
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| [10] |
L. Agong, C. Amarra, J. Caughman, A. Herman, and T. Terada. “On the girth and diameter of generalized Johnson graphs,” Discrete Mathematics, 341 (2018), no. 1, pp.138-142. link |
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| [11] |
Larsen S., Glover E., Bergman A.M., Caughman J. “What kind of opportunities do abstract algebra courses provide for strengthening future teachers’ mathematical knowledge for teaching?” In: Wasserman N. (eds) Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers (pp. 71-84). Research in Mathematics Education (2018), Springer. link |
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| [12] |
J. Caughman, J. Krussel, and J. Mahoney. “Spanning tree decompositions of K2n orthogonal to rotational 1-factorizations,” Graphs and Combinatorics, 33 (2017), no. 2, pp.321-333.
link |
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| [13] |
E. Lockwood, Z. Reed, J. Caughman. “An analysis of statements of the multiplication principle in combinatorics, discrete, and finite mathematics textbooks,” International Journal of Research in Undergraduate Mathematics Education, 3 (2017), pp. 381-416.
link |
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| [14] |
N. Schimanski and J. Caughman. “Cycle structures of orthomorphisms extending partial orthomorphisms of Boolean groups,” Electronic Journal of Combinatorics, 23 (2016), no. 3, Research Papers #P3.41, pp. 1-17.
link |
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| [15] |
E. Lockwood and J. S. Caughman. “Set partitions and the multiplication principle,” Problems, Resources, and Issues in Mathematics Undergraduate Studies, 26 (2016), no. 2, pp. 143-157.
link |
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| [16] |
L. Tran, A. Gronquist, M. Perkowski, J. Caughman. “An improved factorization approach to reversible circuit synthesis based on EXORs of products of EXORs,” Proceedings of the IEEE 46th International Symposium on Multiple-Valued Logic, Sapporo, (2016), pp. 37-43.
link
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| [17] |
R. Dhal, G. Lafferriere, and J. Caughman. “Towards a complete characterization of
vulnerability of networked synchronization processes,” 2016 IEEE 55th Conference on Decision and Control (CDC), Las Vegas, NV (2016)
pp. 5207-5212. link |
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| [18] |
P. Banda, J. Caughman, J. Pospichal. “Configuration symmetry and
performance upper bound of one-dimensional cellular automata for the leader election problem,” Journal of Cellular Automata, 10
(2015), no. 1-2, pp. 1-21.
link |
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| [19] |
E. Lockwood, C. Swinyard, J. S. Caughman. “Patterns, sets of outcomes, and combinatorial justification: two students' reinvention of counting formulas,” International Journal of Research in Undergraduate
Mathematics Education, 1 (2015), no. 1, pp. 1-36.
link |
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| [20] |
E. Lockwood, Z. Reed, J. Caughman. “Categorizing statements of the
multiplication principle,” Proceedings of the 37th Annual Meeting of the North American Chapter of PME,
Michigan State University. (2015). pp. 80-87.
link
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| [21] |
E. Lockwood, C. Swinyard, J. Caughman. “Modeling outcomes in
combinatorial problem solving: the case of combinations,” Proceedings of the 18th Special Interest Group of the MAA on RUME, Pittsburgh, PA: West Virginia University. (2015), pp. 690-696.
link 1
link 2
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| [22] |
J. Caughman, C. Dunn, J. Laison, N. Neudauer, and C. Starr. “Minimum representations of rectangle visibility graphs,” Graph Drawing: 22nd International Symposium, (2014).
link |
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| [23] |
E. Lockwood, C. Swinyard, J. Caughman. “Examining students' combinatorial
thinking through reinvention of basic counting formulas,” Proceedings for the 17th Special Interest Group of the MAA on RUME, Denver, CO: Northern Colorado University. (2014), pp. 169-184.
link |
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| [24] |
E. Johnson, J. Caughman, J. Fredericks, L. Gibson. “Implementing inquiry-oriented curriculum: From the
mathematicians’ perspective,” Journal of Mathematical Behavior, 32 (2013), no. 4, pp. 743-760. |
|
| [25] |
M. Hawash, M. Perkowski, S. Bleiler, J. Caughman, A. Hawash. “Reversible function synthesis of large
reversible functions with no ancillary bits using covering set partitions,” ITNG 8th International Conference, (2011), no. 16, pp. 1008-1013. |
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| [26] |
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. |
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| [27] |
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. |
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| [28] |
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. |
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| [29] |
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. |
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| [30] |
J. S. Caughman IV and J. J. P. Veerman. “Kernels of directed graph Laplacians,” Electron.
J. Combin., 13 (2006), no. 1, Research Papers #R39, pp. 1-8. |
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| [31] |
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. |
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| [32] |
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. |
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| [33] |
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. preprint
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| [34] |
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. |
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| [35] |
G. Lafferriere, J. S. Caughman IV, and A. Williams. “Graph theoretic methods in the
stability of vehicle formations,” Proceedings of the 2004 American Control Conference, Boston, MA, 4 (2004), pp. 3729-3734. |
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| [36] |
J. S. Caughman IV. “Bipartite Q-polynomial distance-regular graphs,” Graphs and Combinatorics, 20 (2004), no. 1, pp.47-57. |
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| [37] |
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, (2004), pp.125-132. |
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| [38] |
J. S. Caughman IV. “The last subconstituent of a bipartite P- and Q-polynomial association
scheme,” European Journal of Combinatorics, 24 (2003), no. 5, pp.459-470. |
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| [39] |
J. S. Caughman IV. “The parameters of bipartite Q-polynomial distance-regular graphs,”
Journal of Algebraic Combinatorics, 15 (2002), no. 3, pp.223-229. |
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| [40] |
B. E. Sagan and J. S. Caughman IV. “The multiplicities of a dual-thin Q-polynomial
association scheme,” Electronic Journal of Combinatorics, 8 (2001), no. 1, #N4, pp. 1-5.
preprint
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| [41] |
J. S. Caughman IV. “Bipartite Q-polynomial quotients of antipodal distance-regular
graphs,” J. Combin. Theory Ser. B, 76 (1999), pp.291-296. |
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| [42] |
J. S. Caughman IV. “The Terwilliger algebras of bipartite P- and Q-polynomial association
schemes,” Discrete Math., 196 (1999), pp.65-95. |
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| [43] |
J. S. Caughman IV. “Spectra of bipartite P- and Q-polynomial association schemes,”
Graphs Combin., 14 (1998), pp.321-343. |
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| [44] |
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, 991 (1997), pp.108-109. |
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| [45] |
J. S. Caughman IV. “Intersection numbers of bipartite distance-regular graphs,” Discrete
Math., 163 (1997), pp.235-241. |
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| WORKS IN PROGRESS: |
| [1] |
J. S. Caughman IV. “The classification of distance-regular graphs that support a spin
model,” in preparation. |
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| [2] |
J. S. Caughman IV and E. Lockwood. “Rotational one-factorizations and multicolored spanning tree decompositions of K2n,” in preparation. |
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