Publications

From REU and EXCEL Programs at Lafayette College

Asterisks denote undergraduate authors.

Summer 2013

  • E. Berkove*, D. Cervantes-Nava*, D. Condon*, R. Katz*, “Automorphisms of S6 and the Colored Cubes Puzzle,” submitted.
  • A. Chin*, G. Gordon, K. MacPhee,* and C. Vincent*, “Pick a tree, any tree,” to appear American Math. Monthly.
  • A. Chin*, G. Gordon, K. MacPhee,* and C. Vincent*, “Random subtrees of complete graphs,” submitted.

Summer 2012

  • Benjamin D. Sokolowsky*, Amy G. VanHooft,* Rachel M. Volkert*, and Clifford A. Reiter, “An Infinite Family of Perfect Parallelepipeds,” Mathematics of Computation, 83 (2014), 2441-2454.
  • J. Cape*, W. Dearden*, W. Gamber*, J. Liebner, Q. Lu, and L Nguyen*, “Estimating Heston’s and Bates’ models parameters using Markov Chain Monte Carlo simulation.”  To appear in the Journal of Statistical Computation and Simulation, 2014.
  • J. Cape*, W. Dearden*, W. Gamber*, and L Nguyen*, “First encounters with option pricing and return simulation,” to appear in the Rose-Hulman Undergraduate Mathematics Journal.
  • J. Cape*, W. Dearden*, W. Gamber*, J. Liebner, Q. Lu, and L Nguyen*, “Statistical Properties of Measures of Risk Adjusted Returns Implied by Option-Pricing Models”, submitted.

Summer 2011

  • John Meier, and Liang Zhang*, “Connectivity at infinity for braid groups on complete graphs,” Homology, Homotopy, and its Applications, 15 (2013), No 1., 303 – 31

Summer 2010

    • Hannah Alpert* and Jennifer Iglesias,* “Length 3 edge-disjoint paths is NP-hard,” Comput. Complexity, 21 (2012), 511–513.
    • Kyle Kalail,* Elizabeth McMahon, Catherine Pelland*, Michael Follett,* and Rob Won,* “Partitions of AG(4,3) into maximal caps,” to appear in Discrete Mathematics.

Summer 2009

      • Donald Chambers, Michael Kelly, Qin Lu, Adam Biesenbach,* Angela King,* Kuni Natsuki,* and Qi Sun,* “CDO Squared: The Case of Subprime Mortgages,” The Journal of Structured Finance, 17 (2011), pp. 96–113.
      • Daniel Allen,* Megan Cream,* Kate Finlay,* John Meier, and Ranjan Rohatgi,* “Complete growth series and products of groups,” New York Journal of Mathematics, 17 (2011), 321-329.
      • Chencong Bao,* Camila Friedman-Gerlicz,* Gary Gordon, Peter McGrath,* and Jessica Vega,* “Matroid automorphisms of the H4 root system,” Congr. Numer. 207 (2011), 141–160.
      • Clifford A. Reiter and Jorge F. Sawyer,* “Perfect Parallelepipeds Exist,” Mathematics of Computation, 80 (2011), 1037-1040.
      • Clifford A. Reiter and Jorge F. Sawyer,* “Generalized Perfect Parallelograms and Their Matrix Generators,” JP Journal of Algebra and Number Theory and Applications, 16 (2010), 1-12.

Summer 2008

      • C. Cooley,* W. Ella,* M. Follett,* E. Gilson,* L. Traldi, “Tied dice. II. Some asymptotic results,” Journal of Combinatorial Mathematics and Combinatorial Computing, 90 (2014), 241- 248.
      • C. Cooley,* W. Ella,* M. Follett,* E. Gilson,* L. Traldi, “The Efron dice voting system,” Social Choice and Welfare, 39 (2012), 931–959.
      • Chu Yue (Stella) Dong,* James T. Long,* Clifford A. Reiter, Corey Staten,* Rytis Umbrasas,* “A cellular model for spatial population dynamics,” Computers & Graphics, 34 (2010), 176-181.
      • Farhan Abedin,* Justin Corvino, Shelvean Kapita,* Haotian Wu,* “On isoperimetric surfaces in general relativity, II,” Journal of Geometry and Physics, 59 (2009), 1453-1460.

Summer 2007

      • B. Shtylla,* L. Traldi, L. Zulli, “On the Realization of Double Occurrence Words,” Discrete Math. 309 (2009), 1769-1773.
      • D. D’Argenio* and C. Reiter, “Families of Nearly Perfect Parallelepipeds,” JP Journal of Algebra, Number Theory and Applications, 9 (2007), 105-111.

Summer 2006

      • J. Tirrell* and C. Reiter, “Matrix Generation of the Diophantine Solutions to Sums of 3 ≤ n ≤ 9 Squares that are Square,” JP Journal of Algebra, Number Theory and Applications, 8 (2007) 69-80.
      • S. Fried,* A. Gerek,* G. Gordon, and A. Perunicic,* “Matroid automorphisms of the root system F4,” Electronic J. Comb. 14 (2007) R78, 12 pp.
      • J. Corvino and H. Wu,* “On the Center of Mass of Isolated Systems,” Classical and Quantum Gravity 25 (2008) 18 pp.
      • B. G. Kronenthal* and L. Traldi, “Tied dice,” Journal of Combinatorial Mathematics and Combinatorial Computing, 68 (2009), 85-96.

Summer 2005

      • C. Reiter and J. Tirrell,* “Pursuing the perfect parallelepiped,” JP Journal of Algebra, Number Theory, and Applications, 6 (2006) 279-294.
      • J. Corvino, A. Gerek,* M. Greenberg,* and B. Krummel,* “On isoperimetric surfaces and general relativity,” Pacific J. Math. 231 (2007) 63-84.
      • K. Ehly* and G. Gordon, “Matroid automorphisms of the root system H3,” Geom. Dedicata, 130 (2007) 149-161.
      • M. Albert,* J. Bratz,* P. Cahn,* T. Fargus,* N. Haber,* E. McMahon, J. Smith,* S. Tekansik,* “Color-permuting automorphisms of Cayley graphs,” Cong. Num., 190 (2008) 161-171. (REU groups for 2001 & 2005).

Summer 2004

      • D. Glasser,* L. McDonnell,* J. Meier, K. Penderghest,* and M. Vacha*, “The geometry of the Dehn complex for a spatial graph,” J. Knot Theory Ramifications, 18 (2009) 1175-1191.
      • E. Berkove, J. Van Sickle,* B. Hummon,* and J. Kogut,* “An Analysis of the (Colored Cubes)3 Puzzle,” Discrete Math., 308 (2008) 1033-1045.
      • D. Eisenstat* and G. Gordon, “Non-isomorphic caterpillars with identical subtree data,” Discrete Math., 306 (2006) 827-830.
      • D. Eisenstat,* G. Gordon, and A. Redlich,* “Combinatorial properties of a rooted graph polynomial,” SIAM J. on Discrete Math., 22 (2008) 776-785.
      • D. Eisenstat,* J. Feder,* G. Francos,* G. Gordon, and A. Redlich,* “Optimality and randomness in rooted graphs,” Discrete Appl. Math., 156 (2008) 746-756.
      • P. Chidyagwai* and C. A. Reiter, “A Local Cellular Model for Growth on Quasicrystals, Chaos,” Chaos, Solitons & Fractals, 24 (2005) 803-812.

Summer 2003

      • B. Shtylla* and L. Zulli, “An extension of the Jones polynomial of classical knots,” Journal of Knot Theory and Its Ramifications, 15 (2006) 81-100.
      • M. H. Dinitz,* J. M. Gold,* T. C. Sharkey,* and L. Traldi, “Graphical representations of clutters,” Ars Combinatoria, 94 (2010), 303–320.
      • R. Root, T. Psemeneki,* R. Cortez, P. Watts, and J. Long, “Heads or Tails? Anterior Thrust Generation in Numerically-Simulated Carangiform Fish,” Journal of Morphology, 260 (2004) 323.
      • Deidra A. Coleman,* Christopher J. Dugan,* Robert A. McEwen,* Clifford A. Reiter, and Tran T. Tang,* “Periods of (Q,R)-Fibonacci Sequences and Elliptic Curves,” The Fibonacci Quarterly, 44 (2006) 59-70.
      • J. Harding, E. Jager,* and D. Smith, “Group-valued measures on the lattice of closed subspaces of a Hilbert space,” Int’l J. of Theoretical Physics, 44 (2005) 539-548.
      • G. Gordon and E. Jager,* “On the location of the root of a network,” Networks, 55 (2010) 181-186.

Summer 2002

      • A. Beste,* D. Leventhal,* Q. Lu, J. Williams,* “Additional analysis on the Markowitz frontier,” submitted.
      • Angela M. Coxe* and Clifford A. Reiter, “Boolean Hexagonal Automata,” Vector, 19 3 (2003) 113-121.
      • Angela M. Coxe* and Clifford A. Reiter, “Fuzzy Hexagonal Automata and Snowflakes,” Computers & Graphics, 27 (2003) 447-454.
      • A. O. Balan* and L. Traldi, “Preprocessing minpaths for sum of disjoint products,” Institute of Electrical and Electronics Engineers Transactions on Reliability, 52 (2003), 289-295.

Summer 2001

      • M. Abouzaid,* J. Alper,* S. DiMauro,* J. Grosslight,* D. Smith, “Common left- and right-hand divisors of a quaternion integer,” J. Pure Appl. Algebra, 217 (2013), 779-785.
      • M. Abouzaid,* J. Alper,* S. DiMauro,* J. Grosslight,* D. Smith, “On cosets of the unit loop of integral octonions,” Communications in Algebra, 35 (2007) 207-214.
      • M. Albert,* J. Bratz,* P. Cahn,* T. Fargus,* N. Haber,* E. McMahon, J. Smith,* S. Tekansik,* “Color-permuting automorphisms of Cayley graphs,” Cong. Num., 190 (2008) 161-171. (REU groups for 2001 & 2005).
      • J. Blasiak,* J. Rowe,* O. Yacobi,* and L. Traldi, “An exposition of elementary matroid theory,” Ars Combinatoria, 77 (2005), 33-44.

Summer 2000

      • Ned W. Allis,* Jeffrey P. Dumont,* and Clifford A. Reiter, “Visualizing point sets, fractals, and quasicrystals using raster techniques,” Computers & Graphics, 25 (2001) 519-527.
      • A. Bailey,* G. Gordon, M. Patton,* J. Scancella*, “Expected value expansions in rooted graphs,” Disc. Appl. Math., 128 (2003) 555-571.
      • J. Loeffler,* J. Meier, and J. Worthington,* “Graph Products and Cannon Pairs,” International Journal of Algebra and Computation, 12 (2002) 747–754.
      • John H. Long, Bruce Adcock,* and Robert G. Root, “Force transmission via axial tendons in undulating fish: a dynamic analysis,” Comparative Biochemistry & Physiology Part A, 133 (2002) 911-929.

Summer 1999

      • Ned Allis,* Jeffrey P. Dumont,* Flynn J. Heiss,* and Clifford A. Reiter, “Fast Fourier Transforms, Diffraction Patterns, and J,” Vector, 16 3 (2000) 111-116.
      • Bruce Adcock,* Kevin C. Jones,* Clifford A. Reiter, and Lisa M. Vislocky,* “Iterated Function Systems with Hyperbolic Symmetry”, Computers & Graphics, 24 (2000) 791-796.

Summer 1998

      • Jeffrey P. Dumont,* Flynn J. Heiss,* Kevin C. Jones,* Clifford A.Reiter, and Lisa M. Vislocky,* “Chaotic Attractors and Evolving Planar Symmetry, Computers & Graphics,” 23 (1999) 613-619.
      • Jeffrey P. Dumont* and Clifford A. Reiter, “Chaotic Attractors Near Forbidden Symmetry,” Chaos, Solitons & Fractals, 11 (2000) 1287-1296.
      • Kevin C. Jones* and Clifford A. Reiter, “Chaotic Attractors with Cyclic Symmetry Revisited,” Computers & Graphics, 24 (2000) 271-282.
      • Jeffrey P. Dumont,* Flynn J. Heiss,* Kevin C. Jones,* Clifford A. Reiter, and Lisa M. Vislocky,* “N-dimensional Chaotic Attractors with Crystallographic Symmetry,” Chaos, Soliton’s and Fractals, 12 (2001) 761-784.
      • Manny Aivaliotis,* Gary Gordon, and William Graveman,* “When bad things happen to good trees,” J. Graph Theory, 37 (2001) 79-99.

Summer 1997

      • Evan Fisher, Matthew Berman,* Natalie Vowels,* and Christine Wilson,* “Excursions of a Normal Random Walk above a Boundary,” Statistics and Probability Letters, 48 (2000), 141-151.
      • Danielle Bianco,* Olivia M. Carducci, Stephen Hartke,* and Anne Larimer,* “Stable matchings in the couples problem,” Morehead Electronic Journal of Applicable Mathematics, Issue 2, MATH-2001-06, January 16, 2002.
      • Nathan C. Carter,* Stephen M. Grimes,* and Clifford A. Reiter, “Frieze and Wallpaper Chaotic Attractors with a Polar Spin,” Computers & Graphics, 22 6 (1998) 765-779.
      • Nathan C. Carter,* Richard L. Eagles,* Stephen M. Grimes,* Andrew C. Hahn,* and Clifford A. Reiter, “Chaotic Attractors with Discrete Planar Symmetries,” Chaos, Solitons & Fractals, 9 12 (1998) 2031-2054.
      • Nathan Carter,* Richard Eagles,* Stephen Grimes,* Andrew Hahn,* and Clifford A. Reiter, “Chaos with Symmetry: Reflections on an Exhibition,” The CDROM Proceedings of the APL97 International Conference on APL, Toronto, Ontario, August 17-20, 1997.
      • Susan Garner Garille* and John Meier, “Whitehead graphs and the S1 invariants of infinite groups,” International Journal of Algebra and Computation, 8 (1998) 23-34.

Summer 1996

      • Lori Fern,* Gary Gordon, Jason Leasure,* Sharon Pronchik,* “Matroid automorphisms and symmetry groups,” Combinatorics, Probability, and Computing, 9 (2000), 105-123.
      • Christina Ahrens,* Gary Gordon, and Elizabeth McMahon, “Finite Convex Sets and the Beta Invariant,” Discrete and Computational Geometry, 22 (1999), 411-424.
      • Christie L. Gilbert,* Joseph D. Kolesar,* Clifford A. Reiter, and John D. Storey,* “Function Digraphs of Quadratic Maps Modulo p,” The Fibonacci Quarterly, 39 1 (2001) 32-49.
      • Sean Grettum,* Jennifer Mandelson,* John Meier, Philippa Mignon Rhodes,* “Automatic Groups, Rational Growth, and Polygonal Amalgams,” Communications in Algebra, 29 (2001) 5371-5382.
      • Elizabeth McMahon, Beth A. Shimkus,* and Jessica Wolfson,* “Chordal graphs and the characteristic polynomial,” Discrete Math., 262 (2003) 211-219.

Summer 1995

      • Jessica Wolfson* and John Meier, “Visualizing the Geometry of Lissajous Knots,” College Mathematics Journal, 28 (1997) 211-216.
      • Nicole Librizzi,* John H. Long, Robert G. Root, “Modeling a swimming fish with an initial-boundary value problem: unsteady maneuvers of an elastic plate with internal force generation,” Mathematical and Computer Modeling, 30 (1999) 77-93.
      • Travis Lee,* Max Minzner,* Evan Fisher, “The length of an excursion above a linear boundary by a random walk,” Statistics and Probability Letters, 34 (1997) 397-402.
      • Travis Lee,* Max Minzner,* Evan Fisher, “Excursions of a random walk related to the strong law of large numbers,” The Rocky Mountain Journal of Mathematics, 28 (1998) 595-606.
      • Gabriel F. Brisson* and Clifford A. Reiter, “Parallel Processing with J,” Vector, 13 1 (1996) 86-95.
      • Gabriel F. Brisson,* Kaj M. Gartz,* Benton J. McCune,* Kevin P. O’Brien,* and Clifford A. Reiter, “Symmetric Attractors in 3D Space,” Chaos, Solitons & Fractals, 7 7 (1996) 1033-1051.

Summer 1994

      • Jessica K. Benashski,* Ryan R. Martin,* Justin T. Moore,* and Lorenzo Traldi, “On the b-invariant for graphs,” Congressus Numerantium, 109 (1995) 211-221.
      • Laura McKinney,* John Meier, and Katherine Schnare,* “Abelian quotients of Artin groups,” Houston Journal of Mathematics, 21 (1995) 659-670.
      • Caroline Lucheta,* Eli Miller,* and Clifford A. Reiter, “Digraphs from powers mod p,” The Fibonacci Quarterly, 34 3 (1996) 226-239.

Summer 1993

      • Sandy D. Balkin,* Deborah S. Cousins,* Christopher K. Orr,* and Clifford A. Reiter, “Short periods of continued fraction convergents modulo m: a generalization of the Fibonacci case,” The Fibonacci Quarterly, 33 3 (1995) 222-233.
      • Sarah Drucker,* Evan Fisher, and Imola Fodor,* ” On random walks and levels of the form na,” The Rocky Mountain Journal of Mathematics, 26 1 (1996) 117-134.
      • Gary Gordon, Eleanor McDonnell,* Darren Orloff,* and Nen Yung, “On the Tutte polynomial of a tree,” Congressus Numerantium, 108 (1995) 141-151.
      • Gary Gordon and Eleanor McDonnell,* “Trees with the same degree sequence and path numbers,” Discrete Mathematics, 147 (1995) 297-300.

Summer 1992

  • Sandy D. Balkin,* Elizabeth L. Golebiewski,* and Clifford A. Reiter, “Rasterization of elliptic curves,” Computers and Graphics, 18 (1994) 837-843.
    • Sandy D. Balkin,* Elizabeth L. Golebiewski,* and Clifford A. Reiter, “Chaos and elliptic curves,” Computers and Graphics, 18 (1994) 113-117.

Arthur D. Gorman

With deep regret and a profound sense of loss we sadly announce the death of our esteemed colleague and dear friend, Arthur D. Gorman, Associate Professor of Mathematics. Professor Gorman died on December 15, here in Easton. He is survived by his two daughters--Anne Gorman of Seattle, Washington and Mary Gorman of State College, Pennsylvania--and by his brother Mark Gorman of Littleton, Colorado.

For more information, please visit the pages below.

Obituary

Remembrances of Art

Calendar of Events

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Contact Us

Gary Gordon
Department Head
229 Pardee Hall
Easton, PA 18042-1778
gordong@lafayette.edu
(610) 330-5275