Mathematics Department

From REU and EXCEL Programs at Lafayette College

Asterisks denote undergraduate authors.

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,” (to appear).
• 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,” to appear in the Journal of Combinatorial Mathematics and Combinatorial Computing.
• 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,” to appear in Ars Combinatoria.
• 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,” to appear in Networks.

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 an integral quaternion,” submitted.
• 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,” to appear in Cong. Num. (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 n^a,” 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.