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), 859869.

The oddeven 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), 655665.

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), 318346.

Combinatorial analysis of diagonal, box, and greaterthan polynomials as
packing functions (with Jose TorresJimenez, Nelson RangelValdez,
and Raghu N. Kacker).

Applied Mathematics and Information Sciences, 9 (2015), 27572766.

The oddeven invariant for graphs
(with Richard Eager).
 European Journal of Combinatorics,
50 (2015), 8796.

Obtaining a trapezoidal distribution (with R. Kacker and R. Kessel).
 Communications in Statistics  Theory and Methods,
44 (2015), 45864599.

Intersections of descending sequences of affinely equivalent convex bodies
.
 Beiträge zur Algebra und Geometrie
54 (2013), 669676.

Caratheodory type results for sums and unions of convex sets (with V. Soltan).
 Rocky Mountain Journal of Math 43 (2013), 16751688.

Combinatorial types of bicyclic polytopes (with T. Bisztriczky).
 Discrete Mathematics 312 (2012), 18631876.

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), 1618.

Enumeration in torus arrangements.
 European Journal of Combinatorics, 32 (2011), 870881.

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), 120126.

On the conjectured upper bounds for entries of mutation count matrices.
 European Journal of Combinatorics, 30, no. 8 (2009), 18961901.

Finite sets as complements of finite unions of convex sets (with W. Morris).
 Discrete and Computational Geometry, 42, no. 2 (2009), 206218.

Rectangular distribution whose width is not exactly known: isocurvilinear
trapezoidal distribution (with R. N. Kacker).

Metrologia, 46 (2009), 254260.

The intersection of convex transversals is a convex polytope (with V. Soltan).

Beiträge zur Algebra und Geometrie, 50, no. 1 (2009), 283294.

Refining the InParameterOrder 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), 287297.

IPOG/IPOD: efficient test generation for
multiway 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), 125148.

IPOG  a general strategy for tway 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 ComputerBased Systems (Washington, D.C., USA), IEEE
Computer Society, 2007, pp. 549556.

Trapezoidal and triangular distributions
for Type B evaluation of standard uncertainty (with R. N. Kacker).

Metrologia, 44 (2007), 117127.

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), 223234.

Three rings of polyhedral simple functions.

Journal of Research of the National Institute of Standards and Technology,
111 (2006), 127134.

Characteristic polynomials,
Ehrhart quasipolynomials, and torus groups.

J. of Number Theory, 17 (2006), 315329

The oddeven invariant of an oriented matroid.

European Journal of Combinatorics. 27 (2006), 806813.

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), 715726.

Oriented matroids and associated valuations.

Discrete and Computational Geometry, 33 (2005), 445462.
Current research 
Oriented matroids. Convexity and combinatorics.
Valuations on classes of polyhedra (e.g., Ehrhart polynomials).
Covering arrays. See
the web page for the project, Automated Combinatorial Testing
for Software
(ACTS), of the National Institute of Standards and
Technology (NIST).
^{*}while sitting in a rocking chair, whittling.