Publications

Publications are listed in reverse chronological order by publication date. Last updated June 28, 2022.

1. G. I. Williams and L. W. Berman. Preface to the 2022 symmetries in graphs, maps and abstract polytopes workshop special issue. The Art of Discrete and Applied Mathematics, 3 2024.

2. L. W. Berman, D. Oliveros, and G. I. Williams. Rotationally symmetric snarks from voltage graphs. Discrete Mathematics, 2024.

3. D. Pellicer and G. I. Williams. On infinite 2-orbit polyhedra in classes 2₀ and 2₂. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Feb 2023.

4. G. Cunningham, M. Mixer, and G. Williams. Reflexible covers of prisms. Contributions to Discrete Mathematics, 2022.

5. Gabe Cunningham, Daniel Pellicer, and Gordon Williams. Stratified operations on maniplexes. Algebraic Combinatorics, 5(2):267–287, 2022. doi: 10.5802/alco.208. 

6. Leah Wrenn Berman, Glenn G. Chappell, Chris Hartman, Jill Faudree, John Gimbel, and Gordon Williams. On graphs with proper connection number 2. Theory and Applications of Graphs, 8(2):Article 2, 2021.

7. E. Schulte, P. Sober ́on, and G. I. Williams. Prescribing symmetries and automorphisms for polytopes. In Polytopes and Discrete Geometry, Contemporary Mathematics, volume 764 of Contemp. Math., pages 221–233, Providence, RI, 2021. Amer. Math. Soc.

8. L. Berman, I. Kov ́acs, and G. Williams. On the flag graphs of regular abstract polytopes: Hamiltonicity and Cayley index. Disc. Math., 343(1):1–16, January 2019.

9. L. W. Berman,  B. Monson, D. Oliveros, and G.I. Williams, Fully truncated simplices and their monodromy groups, Adv. Geom. 18 (2018), no. 2, 193–206.

10. D. Pellicer and G. I. Williams. Pyramids over regular 3-tori. SIAM J. Discrete Math (SIDMA), 32(1):249– 265, January 2018.

11. G. Williams. Branko Grünbaum, geometer. Ars Math. Contemp., 15(1), 2018.

12. L. W. Berman, B. Monson, D. Oliveros, and G. I. Williams. Fully truncated simplices and their monodromy groups. Adv. Geom., 18(2):193–206, April 2018.

13. L. W. Berman, T. Pisanski, and G. I. Williams. Operations on oriented maps. Symmetry, 9(11):274, 1–14, November 2017.

14. L. Berman, G. G. Chappell, J. R. Faudree, J. Gimbel, C. Hartman, and G. I. Williams. Graphs with obstacle number greater than one. Journal of Graph Algorithms and Applications, 21(6):1107–1119, 2017.

15. E. Schulte and G. I. Williams, Polytopes with preassigned automorphism groups, Discrete Comput. Geom. 54 (2015), 444–458.

16. L. Berman, B. Monson, D. Oliveros and G. I. Williams, The monodromy group of the truncated simplex, J. Algebraic Combin. 42 (2015), 745—761, doi:10.1007/s10801-015-0600-7.

17. Leah Wrenn Berman, Mark Mixer, Barry Monson, Deborah Oliveros, and Gordon I. Williams. The monodromy group of the n-pyramid. Discrete Math., 320:55–63, April 2014.

18. B. Monson, D. Pellicer, and G. I. Williams. Mixing and monodromy of abstract polytopes. Trans. of the AMS, 366 2651--2681 (2014).

19. M. Mixer, D. Pellicer, and G. I. Williams. Minimal covers of the Archimedean tilings, part 2. Electron. J. Combin., 2(2):#P20, 2013.

20. D. Pellicer and G. I. Williams. Minimal covers of the Archimedean tilings, part 1. Electron. J. Combin., 19(3):#P6, 2012.

21. M. Hartley, D. Pellicer, and G. I. W. Williams. Minimal covers of the prisms and antiprisms. Discr. Math., 312(20):3046–3058, October 2012.

22. B. Monson, D. Pellicer, and G. I. Williams. The Tomotope. Ars Math. Contemp., 5:355–370, June 2012.

23. L. Berman and G. I. Williams. Kaleidoscopic zonotopal rosettes. Symmetry Cult. Sci., 22(1-2):197–222, 2011.

24. D. Pellicer and G. I. Williams. Quotient representations of uniform tilings. Symmetry Cult. Sci., 22(3- 4):289–306, 2011.

25. M. I. Hartley and G. I. Williams. Representing the sporadic Archimedean polyhedra as abstract polytopes. Discrete Math., 310(12):1835–1844, 2010.

26. L. Berman and G. I. Williams. Euler’s formula. In B. Hopkins, editor, Resources for Teaching Discrete Mathematics, number 74 in MAA Notes. Mathematical Association of America, 2009.

27. G. I. Williams. Using the fractal paintbrush. J. Math. Arts, 3(2):85–96, 2009.

28. G. I. Williams. Petrie schemes. Canad. J. of Math., 57(4):844–870, 2006.

29. L. W. Berman, B. J. Molnar, and G. I. Williams. The cross ratio is the ratio of cross products! Mathematics Magazine, 79(1):54–59, February 2006.

30. J. Mihalisin and G. I. Williams. Nonconvex embeddings of the exceptional simplicial 3-spheres with 8 vertices. J. Comb. Th. (A), 98(1):74–86, 2002.