## 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 S
_{6}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 H
_{4}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 F
_{4},” 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 H
_{3},” 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 S
^{1}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.

- Sandy D. Balkin,* Elizabeth L. Golebiewski,* and Clifford A. Reiter, “Chaos and elliptic curves,” Computers and Graphics,