William J. Keith Michigan Tech University Math Department Tenuretrack Assistant Professor 
Teaching My courses for the fall of 2016 are:


My office hours are MWF 121pm. My office is Fisher 316.  
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 MWF 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. On Tuesdays and Thursdays after class I am typically involved in research activities and unavailable for student meetings. 
I currently serve on the Undergraduate Committee and help organize the Combinatorics Seminar.
Here is the Combinatorics Seminar Schedule for the current semester, with previous schedules back to the Spring of 2013. Seminars this semester run Thursdays 12pm in Fisher 325.
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 and publication list, both in pdf format. 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
I am presently supervising J. T. Davies in research permutation statistics. 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?
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.) I continue with great interest to study more about the polynomials described in the "Ramanujan congruence analogue" paper, which I think are fascinating combinatorial objects with properties that deserve exploration.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 G¨auto;llnitzGordon theorem.
4.) Of the famous problems that interest me, I would name the Borwein Conjecture, on the positivity of coefficients of a series defining a certain weighted sum over specialized partitions, and Lehmer's Conjecture on the nonzeroness of the coefficients of Ramanujan's tau function.