Brant Jones

Department of Mathematics and Statistics
James Madison University
60 Bluestone Drive, MSC 1911
Harrisonburg, VA 22807

email: jones3bc (a t) jmu (d o t) edu

office: 325 Roop Hall, 540 568.3802


I am an Associate Professor at James Madison University. I earned my Ph.D. in mathematics in 2007 from the University of Washington in Seattle and was selected for a three year postdoctoral VIGRE Fellowship at the University of California, Davis before moving to Virginia.

I've mentored over 23 students majoring in math and computer science through various undergraduate research projects. In 2013, I was a visiting researcher in the semester program on Combinatorial Representation Theory at the Institute for Computational and Experimental Research in Mathematics (ICERM). In 2016, I was awarded a sabbatical semester and participated in the workshop on Polyhedral Geometry and Partition Theory at the American Institute of Mathematics (AIM). I currently coordinate our department's William Lowell Putnam Competition team and serve as co-PI (with Anthony Tongen) for the NSF grant that funds our department's summer Research Experiences for Undergraduates (REU) site.

My research interests include games, algorithms, algebraic structures, and enumerative combinatorics, particularly as related to the representation theory of reflection groups. I frequently write computer programs to assist my mathematial work.

I have also had a successful career outside the university, in software engineering/consulting.


Teaching

This semester I am teaching Nature of Mathematics (Math 103) and Stochastic Processes (Math 423).

Some of my previous classes include:

Nature of Mathematics Math 103
Calculus III (Multivariable) Math 237
Graph Theory and Combinatorics Math 353
Advanced Linear Algebra Math 434
Discrete Structures CS/Math 227
Discrete Mathematics Math 245
History of Mathematics Math 415
Topology Math 435
Introductory Calculus Math 205, 231
Elementary Number Theory Math 310
Abstract Algebra I, II Math 430-1
Putnam Problem Solving Seminar Math 485
Calculus I, II Math 235-6


Research

My present work frequently involves undergraduates. If you are a student interested in algorithms/programming or mathematical research, send me an email.

The library of papers is below. Collaborators marked with * are undergraduate researchers.

Opportunity costs in the game of best choice   (with *Madeline Crews, *Kaitlyn Myers, Laura Taalman, *Michael Urbanski, and *Breeann Wilson)
to appear in the Electronic Journal of Combinatorics    math.CO/1903.01821

Weighted games of best choice  
math.CO/1902.10163

Avoiding patterns and making the best choice  
Discrete Mathematics 342 (6) (2019) 1529-1545   math.CO/1812.00963

Positional strategies in games of best choice   (with *Aaron Fowlkes)
to appear in Involve    math.CO/1810.09887

Solitaire Mancala Games and the Chinese Remainder Theorem   (with Laura Taalman and Anthony Tongen)
The American Mathematical Monthly 120 (8) (2013) 706-724    math.CO/1112.3593

The Refined Lecture Hall Theorem via Abacus Diagrams   (with *Laura Bradford, *Meredith Harris, *Alex Komarinski, *Carly Matson, and Edwin O'Shea)
The Ramanujan Journal 34 (2) (2014) 163-176    math.CO/1211.3702

Rational generating series for affine permutation pattern avoidance
Journal of Combinatorics 7 (1) (2016) 51-73    math.CO/1501.03087

Permutations, Pattern Avoidance, and the Catalan Triangle   (with *Derek Desantis, Rebecca Field, *Wesley Hough, *Rebecca Meissen, and *Jacob Ziefle)
Missouri Journal of Mathematical Sciences 25 (1) (2013) 50-60    preprint version

Results and conjectures on simultaneous core partitions   (with Drew Armstrong and Christopher R. H. Hanusa)
European Journal of Combinatorics 41 (2014) 205-220    math.CO/1308.0572

Using carry-truncated addition to analyze add-rotate-xor hash algorithms   (with Rebecca Field)
Journal of Mathematical Cryptology 7 (2) (2013) 97-110    cs.DM/1303.4448

Mask formulas for cograssmannian Kazhdan--Lusztig polynomials   (with Alexander Woo)
Annals of Combinatorics 17 (1) (2013) 151-203    math.CO/1011.1110

Abacus models for parabolic quotients of affine Weyl groups   (with Christopher R. H. Hanusa)
Journal of Algebra 361 (2012), 134-162    math.CO/1105.5333

Affine structures and a tableau model for E6 crystals   (with Anne Schilling)
Journal of Algebra 324 (9) (2010) 2512-2542    math.CO/0909.2442

The enumeration of maximally clustered permutations   (with Hugh Denoncourt)
Annals of Combinatorics 14 (1) (2010) 65-84    math.CO/0704.3469

The enumeration of fully commutative affine permutations   (with Christopher R. H. Hanusa)
European Journal of Combinatorics 31 (5) (2010) 1342-1359    math.CO/0907.0709

An explicit derivation of the Möbius function for Bruhat order  
Order 26 (4) (2009) 319-330    math.CO/0904.4472

A bijection on core partitions and a parabolic quotient of the affine symmetric group   (with Chris Berg and Monica Vazirani)
Journal of Combinatorial Theory, Series A 116 (8) (2009) 1344-1360    math.CO/0804.1380

Leading coefficients of Kazhdan--Lusztig polynomials for Deodhar elements  
Journal of Algebraic Combinatorics 29 (2) (2009) 229-260    math.CO/0711.1391

Kazhdan--Lusztig polynomials for maximally-clustered hexagon-avoiding permutations  
Journal of Algebra 322 (10) (2009) 3459-3477    math.CO/0704.3067

Embedded factor patterns for Deodhar elements in Kazhdan-Lusztig theory   (with Sara C. Billey)
Annals of Combinatorics 11 (3/4) (2007) 285-333    math.CO/0612043


Mathematical Software

Sage: I have contributed some code to sage.combinat, particularly an initial implementation of the Lenart--Postnikov alcove path model for crystals.

liberiksson: A C++ library to perform fast computations on elements of Coxeter groups, used for some of my papers on Kazhdan--Lusztig polynomials. More specifically, the code classifies the Deodhar elements of finite Coxeter groups by embedded factor containment, and verifies that the mu coefficients for Kazhdan--Lusztig polynomials associated to these elements are always 0 or 1.