Jim Lawrence

Department of Mathematical Sciences
George Mason University
Fairfax, VA 22030
lawrence@gmu.edu


"Well, I'm thinking, too. That's important." -- Bret Maverick*


David Hilbert speaks on radio in 1930


Some information for undergraduate students interested in working hard math problems and/or participating in the Virginia Tech math competition or the Putnam competition.


Course web pages (fall, 2017) -

MATH 203, section 004

MATH 641, section 002


Recent publications -

Binary partitions and binary partition polytopes (with George E. Andrews).
Aequat.Math., 91 (2017), 859-869.

The odd-even invariant and Hamiltonian circuits in tope graphs (with Y. Kemper).

On unions and intersections of nested families of cones (with V. Soltan).
Beiträge zur Algebra und Geometrie, 57 (2016), 655--665.

Using combinatorial testing to build navigation graphs for dynamic web applications (with W. Wang, S. Sampath, Y. Lei, R. Kacker, and R. Kuhn).
Software: Testing, Verification, and Reliability, 26 (2016), 318--346.

Combinatorial analysis of diagonal, box, and greater-than polynomials as packing functions (with Jose Torres-Jimenez, Nelson Rangel-Valdez, and Raghu N. Kacker).
Applied Mathematics and Information Sciences, 9 (2015), 2757--2766.

The odd-even invariant for graphs (with Richard Eager).
European Journal of Combinatorics, 50 (2015), 87--96.

Obtaining a trapezoidal distribution (with R. Kacker and R. Kessel).
Communications in Statistics - Theory and Methods, 44 (2015), 4586--4599.

Intersections of descending sequences of affinely equivalent convex bodies .
Beiträge zur Algebra und Geometrie 54 (2013), 669-676.

Caratheodory type results for sums and unions of convex sets (with V. Soltan).
Rocky Mountain Journal of Math 43 (2013), 1675-1688.

Combinatorial types of bicyclic polytopes (with T. Bisztriczky).
Discrete Mathematics 312 (2012), 1863--1876.

Efficient methods for interoperability testing using event sequence testing (with D. R. Kuhn, J. M. Higdon, R. K. Kacker, and Y. Lei).
Crosstalk 25 (2012), 16--18.

Enumeration in torus arrangements.
European Journal of Combinatorics, 32 (2011), 870--881.

A survey of binary covering arrays (with M. Forbes, R. Kacker, R. Kuhn, and Y. Lei).
Electronic Journal of Combinatorics, 18 (2011), Paper 84, 30 pages.

Derivation of isosceles trapezoidal distributions (with R. Kacker).
Measurement Science and Technology, 22 (2011).

Rectangular distribution whose endpoints are not exactly known (with R. Kacker).
Metrologia, 47 (2010), 120--126.

On the conjectured upper bounds for entries of mutation count matrices.
European Journal of Combinatorics, 30, no. 8 (2009), 1896-1901.

Finite sets as complements of finite unions of convex sets (with W. Morris).
Discrete and Computational Geometry, 42, no. 2 (2009), 206-218.

Rectangular distribution whose width is not exactly known: isocurvilinear trapezoidal distribution (with R. N. Kacker).
Metrologia, 46 (2009), 254-260.

The intersection of convex transversals is a convex polytope (with V. Soltan).
Beiträge zur Algebra und Geometrie, 50, no. 1 (2009), 283-294.

Refining the In-Parameter-Order strategy for constructing covering arrays (with M. Forbes, Y. Lei, R. N. Kacker, and D. R. Kuhn).
Journal of Research of the National Institute of Standards and Technology, 113, no. 5 (2008), 287-297.

IPOG/IPOD: efficient test generation for multi-way software testing (with Y. Lei, R. N. Kacker, D. R. Kuhn, and V. Okun).
Journal of Software Testing, Verification, and Reliability, 18, no. 3 (2008), 125-148.

IPOG - a general strategy for t-way software testing (with Y. Lei, R. N. Kacker, D. R. Kuhn, and V. Okun).
In ECBS '07: Proceedings of the 14th Annual IEEE International Conference and Workshops on the Engineering of Computer-Based Systems (Washington, D.C., USA), IEEE Computer Society, 2007, pp. 549--556.

Trapezoidal and triangular distributions for Type B evaluation of standard uncertainty (with R. N. Kacker).
Metrologia, 44 (2007), 117--127.

A counting problem in linear programming.
In Perspectives in Operations Research - Papers in honor of Saul Gass' 80th birthday, ed. Alt, Fu, Golden; Springer (2006), 223--234.

Three rings of polyhedral simple functions.
Journal of Research of the National Institute of Standards and Technology, 111 (2006), 127--134.

Characteristic polynomials, Ehrhart quasi-polynomials, and torus groups.
J. of Number Theory, 17 (2006), 315-329

The odd-even invariant of an oriented matroid.
European Journal of Combinatorics. 27 (2006), 806-813.

Linear independence of Gabor Systems in finite dimensional vector spaces (with G. E. Pfander and D. Walnut).
Journal of Fourier Analysis and Applications, 11 (2005), 715-726.

Oriented matroids and associated valuations.
Discrete and Computational Geometry, 33 (2005), 445-462.


Current research -


*while sitting in a rocking chair, whittling.