## Publications

## From REU and EXCEL Programs at Lafayette College

Asterisks denote undergraduates. A full list of journals that have published articles with Lafayette or REU student co-authors appears at the end of this list.

**Summer 2015**

- Ethan Berkove, Andrew Eickemeyer*, Michael Schulman*, “The 4-Color Cubes Problem,” submitted.
- Ethan Berkove, David Cervantes-Nava*, Daniel Condon*, Andrew Eickemeyer*, Rachel Katz*, Michael Schulman*, “The Color Cubes Puzzle with 2 and 3 Colors,” in progress.

### Summer 2014

- Michael Bauer*, Xiaowen Chang*, Michael Conway*, “Quantifying Options Implications,” SIAM Undergraduate Research Online (SUIRO),
**8**(2015), 177-204. - Michael Bauer*, Don Chambers, Xiaowen Chang*, Jeff Liebner, Qin Lu, “Estimating the Risk Neutral Density of the S&P 500,” submitted.
- Michael Knopf*, Jesse Milzman*, Derek Smith, Dantong Zhu*, Dara Zirlin*, “Lattice Embeddings of Planar Point Sets,” submitted.

### Summer 2013

- Ethan Berkove, David Cervantes-Nava*, Daniel Condon*, Rachel Katz*, “Automorphisms of S
_{6}and the Color Cubes Puzzle,” submitted. - Alex Chin*, Gary Gordon, Kellie MacPhee*, and Charles Vincent*, “Pick a tree, any tree,” American Mathematical Monthly,
**122**(2015), 424-432. - Alex Chin*, Gary Gordon, Kellie MacPhee*, and Charles Vincent*, “Random subtrees of complete graphs,” submitted.
- Edward Gamber, Jeffrey Liebner, and Julie Smith, “The distribution of inflation forecast errors,” Journal of Policy Modeling,
**37**(2015), 47–64. (With Shannon Nitroy*.)

**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. - Joshua Cape*, William Dearden*, William Gamber*, Jeffrey Liebner, Qin Lu, and Linh Nguyen*, “Estimating Heston’s and Bates’ models parameters using Markov Chain Monte Carlo simulation,” Journal of Statistical Computation and Simulation,
**85**(2015), 2295-2314. - Joshua Cape*, William Dearden*, William Gamber*, and Linh Nguyen*, “First encounters with option pricing and return simulation,” Rose-Hulman Undergraduate Mathematics Journal,
**16**(2015) 191-207. - Joshua Cape*, William Dearden*, William Gamber*, Jeffrey Liebner, Qin Lu, and Linh Nguyen*, “Statistical Properties of Measures of Risk Adjusted Returns Implied by Option-Pricing Models,” submitted.
- Emily Dinan*, Alice Nadeau*, and Isaac Odegard*, “Folding Concave Polygons into Convex Polyhedra: The L-Shape,” accepted to the Rose-Hulman Undergraduate Mathematics Journal.

**Summer 2011**

- John Meier, and Liang Zhang*, “Connectivity at infinity for braid groups on complete graphs,” Homology, Homotopy, and its Applications,
**15**(2013), 303-31

**Summer 2010**

- Hannah Alpert* and Jennifer Iglesias*, “Length 3 edge-disjoint paths is NP-hard,” Comput. Complexity,
**21**(2012), 511–513. - Michael Follett*, Kyle Kalail*, Elizabeth McMahon, Catherine Pelland*, and Rob Won*, “Partitions of AG(4,3) into maximal caps,” Discrete Mathematics
**337**(2014), 1-8. - Farhan Abedin* and Justin Corvino, “On the P-scalar curvature,” submitted.

**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), 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 Reiter and Jorge Sawyer*, “Perfect Parallelepipeds Exist,” Mathematics of Computation,
**80**(2011), 1037-1040. - Clifford Reiter and Jorge Sawyer*, “Generalized Perfect Parallelograms and Their Matrix Generators,” JP Journal of Algebra and Number Theory and Applications,
**16**(2010), 1-12.

**Summer 2008**

- Chelsey Cooley*, William Ella*, Michael Follett*, Eric Gilson*, Lorenzo Traldi, “Tied dice. II. Some asymptotic results,” Journal of Combinatorial Mathematics and Combinatorial Computing,
**90**(2014), 241- 248. - Chelsey Cooley*, William Ella*, Michael Follett*, Eric Gilson*, Lorenzo Traldi, “The Efron dice voting system,” Social Choice and Welfare,
**39**(2012), 931–959. - Chu Yue (Stella) Dong*, James Long*, Clifford 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. - Evan Fisher and Shiliang Cui*, “Patterns generated by mth-order Markov Chains”, Statistics and Probability Letters,
**80**(2010) 157–166.

**Summer 2007**

- Daniel D’Argenio* and Clifford Reiter, “Families of Nearly Perfect Parallelepipeds,” JP Journal of Algebra, Number Theory and Applications,
**9**(2007), 105-111.

**Summer 2006**

- Jordan Tirrell* and Clifford 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. - Stephanie Fried*, Aydin Gerek*, Gary Gordon, and Andrijz Perunicic*, “Matroid automorphisms of the root system F
_{4},” Electronic J. Comb.**14**(2007) R78, 12 pp. - Justin Corvino and Haotian Wu*, “On the Center of Mass of Isolated Systems,” Classical and Quantum Gravity
**25**(2008) 18 pp. - Brian Kronenthal* and Lorenzo Traldi, “Tied dice,” Journal of Combinatorial Mathematics and Combinatorial Computing,
**68**(2009), 85-96.

**Summer 2005**

- Clifford Reiter and Jordan Tirrell*, “Pursuing the perfect parallelepiped,” JP Journal of Algebra, Number Theory, and Applications,
**6**(2006) 279-294. - Justin Corvino, Aydin Gerek*, Michael Greenberg*, and Brian Krummel*, “On isoperimetric surfaces and general relativity,” Pacific J. Math.
**231**(2007) 63-84. - Kevin Ehly* and Gary Gordon, “Matroid automorphisms of the root system H
_{3},” Geom. Dedicata,**130**(2007) 149-161. - Melanie Albert*, Jenna Bratz*, Patricia Cahn*, Timothy Fargus*, Nicholas Haber*, Elizabeth McMahon, Jaren Smith*, and Sarah Tekansik*, “Color-permuting automorphisms of Cayley graphs,” Cong. Num.,
**190**(2008) 161-171. (REU groups for 2001 & 2005). - R. E. Andersen*, A. O. Balan*, J. P. Rowe*, and L. Traldi, “A note on independent-disjoint analysis of network reliability,” Applied Mathematical and Computational Sciences
**1**(2010), 61-66.

**Summer 2004**

- David Glasser*, Lori McDonnell*, John Meier, Kevin Penderghest*, and Mary. Vacha*, “The geometry of the Dehn complex for a spatial graph,” J. Knot Theory Ramifications,
**18**(2009) 1175-1191. - Ethan Berkove, Jenna Van Sickle*, Ben Hummon*, and Joy Kogut*, “An Analysis of the (Colored Cubes)
^{3}Puzzle,” Discrete Math.,**308**(2008) 1033-1045. - David Eisenstat* and Gary Gordon, “Non-isomorphic caterpillars with identical subtree data,” Discrete Math.,
**306**(2006) 827-830. - David Eisenstat*, Gary Gordon, and Amanda Redlich*, “Combinatorial properties of a rooted graph polynomial,” SIAM J. on Discrete Math.,
**22**(2008) 776-785. - David Eisenstat*, Jennifer Feder*, Greg Francos*, Gary Gordon, and Amanda Redlich*, “Optimality and randomness in rooted graphs,” Discrete Appl. Math.,
**156**(2008) 746-756. - Prince Chidyagwai* and Clifford Reiter, “A Local Cellular Model for Growth on Quasicrystals, Chaos,” Chaos, Solitons & Fractals,
**24**(2005) 803-812. - Blerta Shtylla*, Lorenzo Traldi, and Louis Zulli, “On the Realization of Double Occurrence Words,” Discrete Math.
**309**(2009), 1769-1773.

**Summer 2003**

- Blerta Shtylla* and Louis Zulli, “An extension of the Jones polynomial of classical knots,” Journal of Knot Theory and Its Ramifications,
**15**(2006) 81-100. - Michael Dinitz*, Jonah Gold*, Thomas Sharkey*, and Lorenzo Traldi, “Graphical representations of clutters,” Ars Combinatoria,
**94**(2010), 303–320. - Robert Root, Tiffany Psemeneki*, Ricardo Cortez, Philip Watts, and John Long, “Heads or Tails? Anterior Thrust Generation in Numerically-Simulated Carangiform Fish,” Journal of Morphology,
**260**(2004) 323. - Deidra Coleman*, Christopher Dugan*, Robert McEwen*, Clifford Reiter, and Tran Tang*, “Periods of (Q,R)-Fibonacci Sequences and Elliptic Curves,” The Fibonacci Quarterly,
**44**(2006) 59-70. - John Harding, Ekaterina Jager*, and Derek Smith, “Group-valued measures on the lattice of closed subspaces of a Hilbert space,” Int’l J. of Theoretical Physics,
**44**(2005) 539-548. - Gary Gordon and Ekaterina 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 Coxe* and Clifford Reiter, “Boolean Hexagonal Automata,” Vector,
**19**3 (2003) 113-121. - Angela Coxe* and Clifford Reiter, “Fuzzy Hexagonal Automata and Snowflakes,” Computers & Graphics,
**27**(2003) 447-454. - Alexandru Balan* and Lorenzo Traldi, “Preprocessing minpaths for sum of disjoint products,” Institute of Electrical and Electronics Engineers Transactions on Reliability,
**52**(2003), 289-295.

**Summer 2001**

- Mohammed Abouzaid*, Jarod Alper*, Steve DiMauro*, Justin Grosslight*, Derek Smith, “Common left- and right-hand divisors of a quaternion integer,” J. Pure Appl. Algebra,
**217**(2013), 779-785. - Mohammed Abouzaid*, Jarod Alper*, Steve DiMauro*, Justin Grosslight*, Derek Smith, “On cosets of the unit loop of integral octonions,” Communications in Algebra,
**35**(2007) 207-214. - Melanie Albert*, Jenna Bratz*, Patricia Cahn*, Timothy Fargus*, Nicholas Haber*, Elizabeth McMahon, Jaren Smith*, and Sarah Tekansik*, “Color-permuting automorphisms of Cayley graphs,” Cong. Num.,
**190**(2008) 161-171. (REU groups for 2001 & 2005). - Jonah Blasiak*, Jennifer Rowe*, Oded Yacobi*, and Lorenzo Traldi, “An exposition of elementary matroid theory,” Ars Combinatoria,
**77**(2005), 33-44.

**Summer 2000**

- Ned Allis*, Jeffrey Dumont*, and Clifford Reiter, “Visualizing point sets, fractals, and quasicrystals using raster techniques,” Computers & Graphics,
**25**(2001) 519-527. - Alison Bailey*, Gary Gordon, Matthew Patton*, Jennifer Scancella*, “Expected value expansions in rooted graphs,” Disc. Appl. Math.,
**128**(2003) 555-571. - Joseph Loeffler*, John Meier, and James Worthington*, “Graph Products and Cannon Pairs,” International Journal of Algebra and Computation,
**12**(2002) 747–754. - John Long, Bruce Adcock*, and Robert 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 Dumont*, Flynn Heiss*, and Clifford A. Reiter, “Fast Fourier Transforms, Diffraction Patterns, and J,” Vector,
**16**3 (2000) 111-116. - Bruce Adcock*, Kevin Jones*, Clifford Reiter, and Lisa Vislocky*, “Iterated Function Systems with Hyperbolic Symmetry”, Computers & Graphics,
**24**(2000) 791-796.

**Summer 1998**

- Jeffrey Dumont*, Flynn Heiss*, Kevin Jones*, Clifford Reiter, and Lisa M. Vislocky*, “Chaotic Attractors and Evolving Planar Symmetry, Computers & Graphics,”
**23**(1999) 613-619. - Jeffrey Dumont* and Clifford Reiter, “Chaotic Attractors Near Forbidden Symmetry,” Chaos, Solitons & Fractals,
**11**(2000) 1287-1296. - Kevin Jones* and Clifford Reiter, “Chaotic Attractors with Cyclic Symmetry Revisited,” Computers & Graphics,
**24**(2000) 271-282. - Jeffrey Dumont*, Flynn Heiss*, Kevin Jones*, Clifford Reiter, and Lisa 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 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 Carter*, Stephen Grimes*, and Clifford Reiter, “Frieze and Wallpaper Chaotic Attractors with a Polar Spin,” Computers & Graphics,
**22**6 (1998) 765-779. - Nathan Carter*, Richard Eagles*, Stephen Grimes*, Andrew 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 Gilbert*, Joseph Kolesar*, Clifford Reiter, and John 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 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 Long, Robert 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 Brisson* and Clifford Reiter, “Parallel Processing with J,” Vector,
**13**1 (1996) 86-95. - Gabriel Brisson*, Kaj Gartz*, Benton McCune*, Kevin O’Brien*, and Clifford Reiter, “Symmetric Attractors in 3D Space,” Chaos, Solitons & Fractals,
**7**7 (1996) 1033-1051.

**Summer 1994**

- Jessica Benashski*, Ryan Martin*, Justin Moore*, and Lorenzo Traldi, “On the β-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 Balkin*, Deborah Cousins*, Christopher Orr*, and Clifford 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 Balkin*, Elizabeth Golebiewski*, and Clifford Reiter, “Rasterization of elliptic curves,” Computers and Graphics,
**18**(1994) 837-843. - Sandy Balkin*, Elizabeth Golebiewski*, and Clifford Reiter, “Chaos and elliptic curves,” Computers and Graphics,
**18**(1994) 113-117.

**List of Journals**

Ars Combinatoria; Chaos, Solitons & Fractals; Classical and Quantum Gravity; College Mathematics Journal; Combinatorics, Probability, and Computing; Communications in Algebra; Comparative Biochemistry & Physiology Part A; Computational Complexity ; Computers & Graphics; Congressus Numerantium; Discrete Applied Mathematics; Discrete Mathematics; Discrete and Computational Geometry; Electronic Journal of Combinatorics; Fibonacci Quarterly; Geometriae Dedicata; Houston Journal of Mathematics; IEEE Transactions on Reliability; Institute of Electrical and Electronics Engineers Transactions on Reliability; International Journal of Algebra and Computation; International Journal of Theoretical Physics; Journal of Combinatorial Mathematics and Combinatorial Computing; Journal of Knot Theory Ramifications; Journal of Geometry and Physics; Journal of Graph Theory; Journal of Morphology; Journal of Pure and Applied Algebra; Journal of Statistical Computation and Simulation; Journal of Structured Finance; JP Journal of Algebra and Number Theory and Applications; Mathematical and Computer Modeling; Mathematics of Computation; Morehead Electronic Journal of Applicable Mathematics; Networks; New York Journal of Mathematics; Pacific Journal of Mathematics; Rose-Hulman Undergraduate Mathematics Journal; SIAM Journal on Discrete Mathematics; SIAM Undergraduate Research Online; Statistics and Probability Letters; The Rocky Mountain Journal of Mathematics; and Vector.