Gary Gordon's Publications

Updated December, 2016

By the way, if your name appears on this page, then your Erdös number is at most 3 (thanks to Bruce Reznick for pointing this out). Or 4. Or 5. The AMS webpage Collaboration Distance lets you quickly compute the distance betweeen any two authors.

The Joy of SET: The Many Mathematical Dimensions of a Seemingly Simple Card Game (with Liz McMahon, Hannah Gordon and Rebecca Gordon) - published November 2016. This book pulls together lots of math about the card game SET, and writing it was a very enjoyable family project.

Matroids: A Geometric Introduction (with J. McNulty) - published Aug. 2012. This is a gentle introduction to matroid theory, written jointly with Jenny McNulty of U. Montana. Please send comments, corrections, and compliments.

Matroid Book

"Constructing prime-field planar configurations," Proc. Am. Math.Soc. 91 (1984), 492-502.  MR 85m:05032

"Matroids over Fp which are rational excluded minors," Discrete Math. 52 (1984) 51-65. MR 85k:05033

(with E. McMahon) Complete Solutions Manual for Calculus, Wadsworth, Belmont, CA (1987)

"Algebraic characteristic sets of matroids," J. Comb. Theory (B) 44 (1988) 64-74. MR 89c:05024

(with E. McMahon) "A greedoid polynomial which distinguishes rooted arborescences," Proc. Am. Math.Soc. 107 (1989), 287-298. MR 90a:05046

(with L. Traldi) "Generalized activities and the Tutte polynomial," Discrete Math. 85 (1990) 167-176. MR 91m:05052

(with S. Chaudhary*) "Tutte polynomials for trees," J. Graph Theory 15 (1991) 317-331. MR 92g:05068

"A Tutte polynomial for partially ordered sets," J. Comb. Theory (B) 59 (1993) 132-155. MR 94e:05073

(with L. Traldi) "Polynomials for directed graphs," Congressus Numerantium 94 (1993) 187-201. MR 95d:05059
        Addendum Congressus Numerantium 100 (1994) 5-6. MR 1 382 300

"Workable gears, Archimedian solids and planar bipartite graphs," American Mathematical Monthly 101 (1994) 527-534. MR 95h:05129

(with E. McDonnell*) "Trees with the same degree sequence and path numbers," Discrete Math. 147 (1995) 297-300. MR 96g:05043

(with E. McDonnell*, D. Orloff*, N. Yung*) "On the Tutte polynomial of a tree," Congressus Numerantium 108 (1995) 141-151. MR 96j:05036

"Series-parallel posets and the Tutte polynomial," Discrete Math. 158 (1996) 63-75. MR 97h:06007

"Using Wallpaper groups to motivate group theory," PRIMUS. VI (1996) 355-365.

(with E. McMahon) "A greedoid characteristic polynomial," Contemp. Math. 197 (1996) 343-351. MR 97f:05040

(with E. McMahon) "Interval partitions and activities for the greedoid Tutte polynomial," Adv. in Applied Math. 18 (1997) 33-49. MR 97k:05048

"A Beta invariant for greedoids and antimatroids," Electronic J. Comb. 4 (1997) R13 13 pages. MR 98a:05044

"Hyperplane arrangements, hypercubes and graphic objects," Congressus Numerantium 126 (1997) 65-72. MR 98j:05038

(with C. Ahrens* and E. McMahon) "Convexity and the beta invariant," Discrete and Computational Geometry 22 (1999) 411-424. MR 2000j:52007

"The answer is 2nn!  What's the question?" American Mathematical Monthly 106 (1999) 636-645. MR 2000j:05050

"The Tutte Polynomial," Encyclopedia of Mathematics, Supplement II, Kluwer Academic Publishers, 2000. This is now available online through SpringerLink.

(with L. Fern*, J. Leasure* and S. Pronchik*) "Matroid automorphisms and symmetry groups," Combinatorics, Probability & Computing 9 (2000), 105-123. MR 2001g:05034

(with E. McMahon) "A characteristic polynomial for rooted graphs and rooted digraphs," Discrete Math. 232 (2001) 19-33. MR 2002b:05126

(with M. Aivaliotis* and W. Graveman*) "When bad things happen to good trees," J. Graph Theory 37 (2001) 79-99. MR 2002j:05037

(with E. McMahon) "Orthogonal Latin Garage Doors," FOCUS 21 (2001) 4-5.

"Using geometry to teach group theory," in Innovations in Teaching Abstract Algebra, Allen Hibbard and Ellen Maycock (eds.), MAA Notes 60 (2002).

(with A. Bailey*, M. Patton* and J. Scanscella*) "Expected value expansions in rooted graphs," Discrete Applied Math. 128 (2003) 555-571. MR 2004e:90030

"Expected rank in antimatroids," Adv. in Applied Math. 32 (2004) 299-318. MR 2005f:05033

"Lafayette College Math REU: Reaching for the asteroid belt," Math Horizons, November (2004) 24-25.

(with E. McMahon) "10002 years of Math Bowl at Lafayette," Math Horizons, November (2005) 10-11.

(with D. Eisenstat*) "Non-isomorphic caterpillars with identical subtree data," Discrete Math. 306 (2006) 827-830.

"Lafayette College's REU," Proceedings of the Conference on Promoting Undergraduate Research in Mathematics, American Mathematical Society, (2007) 91-96.

(with D. Kalman, E. McMahon, R. Nelson and B. Reznick) "Mathematical Enquirer" Math Horizons 14, April 2007, 17-20.

Lafayette College's REU, CUR Quarterly, 28 (Fall 2007) 6-11.

(with K. Ehly*) "Matroid automorphisms of the root system H3," Geom. Dedicata 130 (2007) 149-161.

(with S. Fried*, A. Gerek*, and A. Perunicic*), "Matroid automorphisms of the F4 root system," Electronic J. Comb. 14 (2007) R78, 12 pages.

(with D. Eisenstat* and Amanda Redlich*) "Combinatorial properties of a rooted graph polynomial," SIAM J. on Discrete Math. 22 (2008) 776-785.

(with D. Eisenstat*, J. Feder*, G. Francos* and Amanda Redlich*) "Expected Rank and Randomness in Rooted Graphs," Discrete Appl. Math. 156 (2008) 746-756.

Chromatic and Tutte polynomials for graphs, rooted graphs and trees, Graph Theory Notes of New York LIV (2008) 39-50.

(with E. Jager*) "Distinguished vertices in probabilistic rooted graphs," Networks 55 (2010) 181-186.

(with E. McMahon) "Moving faces to other places: Facet derangements," American Mathematical Monthly, 117 (2010) 865-880. [arXiv version]

(with Chencong Bao*, Camila Friedman-Gerlicz*, Peter McGrath*, and Jessica Vega*), ""Matroid automorphisms of the H4 root system," Congressus Numerantium 207 (2011), 141-160. [arXiv version]

"Matroid representation, geometry and matrices, published in: MAA Notes for "What is a Matroid? Theory and Applications, from the Ground Up" Short Course, New Orleans, January, 2011.

Guest Editor with J. Oxley: "Matroids, Polynomials and Enumeration," Special Volume of Europ. J. Combinatorics, 32 no. 6, (2011).

(with J. McNulty) "Thomas H. Brylawski (1944 - 2007)," Europ. J. Combinatorics, 32 (2011) 712-721.

"On Brylawski's generalized duality," Math. in Comp. Sci., 6 (2012) 135-146.

"Linear relations for a generalized Tutte polynomial," Electronic J. Comb. 22 (2015) P1.79, 30 pages.

(with A. Chin*, K. MacPhee* and C. Vincent*) "Pick a tree, any tree," American Mathematical Monthly, 122 (2015) 424-432.

(with E. McMahon) "Error detection and correction using SET," in The Mathematics of Various Entertaining Subjects: Research in Recreational Math, Jennifer Beineke & Jason Rosenhouse ed., Princeton University Press, 2015.

(with J. McNulty and N. Neudauer) "Fixing numbers for matroids," Graphs and Combinatorics. [arXiv version] 32 (2016) 133-146.

(with A. Chin*, K. MacPhee* and C. Vincent*) "Subtrees of graphs," submitted.

(with E. McMahon) "Non-matroidal generalizations of the Tutte polynomial," submitted as a chapter in Tutte Polynomial Handbook, CRC Press.

"Matroid Representations," submitted as a chapter in A Short Course in Matroid Theory, MAA Press.


* undergraduate co-author.
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