Publications

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 2018

• Amy Pitts*, Kathryn Haglich*, Sarah Neitzel*, Jeffrey Liebner. “A Bayesian method for locating breakpoints in time series”. Joint Mathematics Meetings, MAA General Contributed Paper Session on Modeling and Applications, III.

• Carl Hammarsten, Rae Helmreich*, Anchala Krishnan*, John Meier, and Nathan Schmitz*. “Persistent Homology and Random Models of the Gaussian Primes.” Topology Proceedings

• Dylan Green*. Maximum proper diameter for 2-connected graphs. Dylan Green: Talk “Maximum properdiameter for 2-connected graphs,” National Conference on Undergraduate Research (NCUR), Kennesaw State University.

• Laura Seaberg*. “Intersections of Shortest Taxicab Paths in the Sierpiński Carpet.” Nebraska Conference for Undergraduate Women in Mathematics.

• Rebekah Chase*, Ryan Mike*, Laura Seaberg*. “Intersections of Shortest Taxicab Paths in the Sierpiński Carpet.” Joint Mathematics Meetings, AMS-MAA-SIAM Special Session on Research in Mathematics by Undergraduates and Students in Post-Baccalaureate Programs, II.

• Rebekah Chase*. “Intersections of Shortest Taxicab Paths in the Sierpiński Carpet.” MAKO Undergraduate Mathematics Research Conference at Missouri State University.

Summer 2017

• Allison J. Ganger*, Shannon N. Golden*, Brian G. Kronenthal, Carter A. Lyons*, “On the girth of two-dimensional real algebraically defined graphs,” Discrete Mathematics, online December 3, 2018.
• Joshua D. Nolan*, Clifford A. Reiter, “Computing and Visualizing 3-Dimensional Quasicrystals,” Fractals, to appear
• Carl Hammarsten, Rae Helmreich, Anchala Krishnan, John Meier, and Nathan Schmitz, “Persistent homology and random models of the Gaussian primes,” Topology Proceedings, to appear.

Summer 2015

• Ethan Berkove, Andrew Eickemeyer*, Michael Schulman*, “The 4-Color Cubes Problem,” Integers (2018), Paper No. A68, 23 pages.
• Ethan Berkove, David Cervantes-Nava*, Daniel Condon*, Andrew Eickemeyer*, Rachel Katz*, Michael Schulman*, “The Color Cubes Puzzle with 2 and 3 Colors,” MOVES Volume II (Princeton University Press), 2017.

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,” Discrete & Computational Geometry, 56 (2016), 693-710.

Summer 2013

• Ethan Berkove, David Cervantes-Nava*, Daniel Condon*, Rachel Katz*, “Automorphisms of \(S_6\) and the Color Cubes Puzzle,” Australasian. Journal of Combinatorics,  68 (2017), 71 – 93.
• Alex Chin*, Gary Gordon, Kellie MacPhee*, and Charles Vincent*, “Pick a tree, any tree,” American Mathematical Monthly, 122 (2015), 424-432.  (Winner of a 2016 Paul R. Halmos – Lester R. Ford Award for expository excellence.)
• Alex Chin*, Gary Gordon, Kellie MacPhee*, and Charles Vincent*, “Subtrees of graphs,” J. Graph Theory, 89 (2018), 413 – 438.
• Edward Gamber, Jeffrey Liebner, and Julie Smith, “The distribution of inflation forecast errors,” Journal of Policy Modeling, 37 (2015), 47–64.  (With significant assistance from 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,” The Journal of Geometric Analysis, 27 (2017), no. 2, 1589-1623.

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 H4 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 H3,” 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 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 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 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 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

American Mathematical Monthly; Ars Combinatoria; Australasian Journal of Combinatorics; 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; Fractals; Geometriae Dedicata; Homology, Homotopy, and its Applications; Houston Journal of Mathematics; IEEE Transactions on Reliability; Institute of Electrical and Electronics Engineers Transactions on Reliability; Integers; 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 Geometrical Analysis; Journal of Geometry and Physics; Journal of Graph Theory; Journal of Morphology; Journal of Policy Modeling; 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.