

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 a 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 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). In 2019, I led a Research Experiences for Undergraduate Faculty (REUF) workshop at ICERM.
In 2021, a paper I coauthored with Laura Taalman and Anthony Tongen was cited by Don Knuth in The Art of Computer Programming (volume 4, prefascicle 14a on bipartite matching).
I currently coordinate our department's William Lowell Putnam Competition team and serve as PI (together with Hala Nelson) 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 and have had a successful career outside the university in software engineering/consulting.

Teaching
Some of my previous classes include:
Nature of Mathematics (Strategy and Games) Math 103 
Calculus III (Multivariable) Math 237 
Stochastic Processes Math 423 
Introductory Calculus Math 205, 231 
Discrete Mathematics Math 245 
Abstract Algebra I, II Math 4301 
Elementary Statistics Math 220 
Elementary Number Theory Math 310 
Advanced Linear Algebra Math 434 
Discrete Structures CS/Math 227 
Graph Theory and Combinatorics Math 353 
Topology Math 435 
Calculus I, II Math 2356 
History of Mathematics Math 415 
Putnam Problem Solving Seminar Math 485 
Presentation
Spring MAA MDDCVA section meeting April 13, 2019 (
transcript)
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.
Strategyindifferent games of best choice (with Katelynn D. Kochalski, Sarah Loeb and Julia C. Walk)
Weighted games of best choice
Opportunity costs in the game of best choice (with *Madeline Crews, *Kaitlyn Myers, Laura Taalman, *Michael Urbanski, and *Breeann Wilson)
Avoiding patterns and making the best choice
Positional strategies in games of best choice (with *Aaron Fowlkes)
Rational generating series for affine permutation pattern avoidance
Results and conjectures on simultaneous core partitions (with Drew Armstrong and Christopher R. H. Hanusa)
The refined lecture hall theorem via abacus diagrams (with *Laura Bradford, *Meredith Harris, *Alex Komarinski, *Carly Matson, and Edwin O'Shea)
Solitaire Mancala Games and the Chinese Remainder Theorem (with Laura Taalman and Anthony Tongen)
Permutation pattern avoidance and the Catalan triangle (with *Derek Desantis, Rebecca Field, *Wesley Hough, *Rebecca Meissen, and *Jacob Ziefle)
Using carrytruncated addition to analyze addrotatexor hash algorithms (with Rebecca Field)
Mask formulas for cograssmannian KazhdanLusztig polynomials (with Alexander Woo)
Abacus models for parabolic quotients of affine Weyl groups (with Christopher R. H. Hanusa)
Affine structures and a tableau model for E_{6} crystals (with Anne Schilling)
The enumeration of fully commutative affine permutations (with Christopher R. H. Hanusa)
The enumeration of maximally clustered permutations (with Hugh Denoncourt)
An explicit derivation of the Möbius function for Bruhat order
A bijection on core partitions and a parabolic quotient of the affine symmetric group (with Chris Berg and Monica Vazirani)
Leading coefficients of KazhdanLusztig polynomials for Deodhar elements
KazhdanLusztig polynomials for maximallyclustered hexagonavoiding permutations
Embedded factor patterns for Deodhar elements in KazhdanLusztig theory (with Sara C. Billey)
Mathematical Software
Sage: I have contributed some code to
sage.combinat, particularly an initial implementation of the LenartPostnikov 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 KazhdanLusztig polynomials. More specifically, the code classifies the Deodhar elements of finite Coxeter groups by embedded factor containment, and verifies that the mu coefficients for KazhdanLusztig polynomials associated to these elements are always 0 or 1.