William J. Keith Michigan Tech University Math Department Associate Professor 
Teaching My courses for the Fall of 2021 are:


My regular office hours are T Th 12pm  1pm. My office is Fisher 314, but this semester I will old office hours in my Zoom office, https://michigantech.zoom.us/j/7738766078. Should students have class during this hour I warmly encourage making an appointment for a more convnient time to meet.  
Outside of my office hours, students should get in touch with me using my MTU email, wjkeith [at] mtu.edu (no spaces). I am generally available at other times if a student emails me well in advance. This and other class information is available on the syllabus for each class, which is also on the course webpages linked above. 
I currently serve on the Undergraduate Committee and am the advisor for math majors with the Discrete Mathematics concentration. I also help organize the Algebra and Combinatorics Seminar.
Here is the Algebra and Combinatorics Seminar schedule for the current semester, with previous schedules back to the Spring of 2013. The Seminar is not running in the Fall of 2020.
My research is in combinatorics, specializing in partition theory and related qseries and identities.
For the standard outline of my research, please help yourself to a copy of my CV which includes a full publication list. For more detail, I list below a few of my papers (and my thesis). Preprints of all my work are available on the arXiv. 
Selected Publications and Preprints
Graduate Students
In 20162017 I supervised the master's thesis of J. T. Davies in research permutation statistics. Mr. Davies is currently in doctoral study at the University of Waterloo in Canada. Our motivating question: the major index is symmetric over some sets of patternavoiding permutations in S_{n} with fixed descent number, and (maj, des) form a Mahonian pair. Are there conditions analogous to pattern avoidance (and hopefully equally interesting) for other pairs such as (den, exc) which are known to be Mahonian but are not distributed symmetrically over patternavoidance classes?
I am presently advising Master's student Emily Anible.
If graduate students are interested in research with me they should let me know. I am presently open to becoming a graduate advisor for a new student.
Ongoing Research
These are a few of the ongoing research questions which interest me. I am always happy to receive comments from interested colleagues, and would be pleased to collaborate with someone who has useful ideas in these directions. Graduate students considering combinatorics who find some of these questions interesting are encouraged to contact me as well.
1.) My most immediate current project is extending the refinement of Stanley's formula listed given in the first listed paper. I think it would be an exciting result if this could be generalized to standard Young tableaux of any shape.2.) I am interested in mregular partitions, especially their lowmodulus congruences. Related to this, I would like to show properties of singular overpartitions related to known theorems such as the PakPostnikov (m,c) theorem.
3.) I have recently been studying Kanade and Russell's very curious conjectures on asymmetric versions of the GöllnitzGordon theorem.
4.) Dousse and Kim's conjectures on unimodality for the overpartition analogue of the Gaussian coefficients seems quite interesting to me.
5.) Bergeron's ad  bc conjecture.