
My General Research Interests
My field of research is enumerative and algebraic combinatorics, with interests in rook
theory, pattern avoidance, permutation statistics, Stirling numbers, generating
functions, and partition theory.
My Ph.D. was conferrred on June 18th, 2006 from the University of California, San Diego.
Thesis: A General Rook Model For Product Formulas & PolyStirling Numbers
Thesis Advisor: Dr. Jeff Remmel , UC, San Diego
My CV
My CV as of 1/20/2021.
My Publications
 ``Improving foresight predictions in the 2002–2018 NFL regularseasons: A classic tale of quantity vs. quality"  .pdf
 Journal of Advances in Mathematics and Computer Science 34(12) (2019) : DOI
 Coauthor: E. C. Balreira
 ``Shift equivalence in the generalized factor order"  arXiv pdf
 Archiv der Mathematik (2018): DOI
 Coauthors: J. Fidler (formerly Emery, TU student, Class of 2008), D. Glasscock, J. Pantone, & M. Xu
 ``Generating functions and Wilf equivalence for generalized interval embeddings"  .pdf
 Australasian Journal of Combinatorics, 64(1) (2016), pp. 44–60
 Coauthors: R. Chamberlain, G. Cochran (TU student, Class of 2013), S. Ginsburg, M. Riehl, & C. Zhang
 ``Connection coeffcients between rising & falling factorial bases"  .pdf
 Annals of Combinatorics, 19.2 (2015), pp. 337–361
 Coauthors: J. Liese & J. Remmel
 ``A combinatorial proof of a theorem of Katsuura"  .pdf
 College Journal of Mathemtics, 45 (2014), No. 5, pp. 365–369
 ``An Oracle method to predict NFL games"  .pdf
 Journal of Quantitative Analysis of Sports, 10 (2014), No. 2, pp. 183–196
 Coauthors: E. C. Balreira & T. Tegtmeyer
 ``Minimal Overlapping Embeddings & Exact Matches in Words"  .pdf
 Pure Mathematics and Applications  Algebra and Theoretical Computer Science,
23 (2012), No. 3, pp. 291–315
 Coauthor: J. Remmel
 ``Two qAnalogues of PolyStirling Numbers"  .pdf
 Journal of Integer Sequences 14 (2011), 11.9.6
 ``What I Learned from Being on Search Committees: Tips on Applying to Teaching Schools" 
web version
 MAA Focus 30.4 (2010), pp. 23
 ``mPartition Boards & PolyStirling Numbers"  .pdf
 Journal of Integer Sequences 13 (2010), 10.3.3
 ``Augmented Rook Boards & General Product Formulas"  .pdf
 Electronic Journal of Combinatorics 15 (2008), R85
 Coauthor: J. Remmel
Some Recent Research Talks (* = invited talk)
 A,BMinimal Stirling Numbers  Permutation Patterns  7/9/18 at Dartmouth College
 Statistics on Set Partitions  British Combinatorics Conference  6/3/17 at the University of Strathclyde
in Glasgow, UK
 Combinatorial Enumeration in Pascal's Trinagle  Undergraduate Mathematics Colloquium*  2/17/17 at Rice University
in Houston, TX
 generatingfunctionology  Mathematical Seminar Series*  5/09/16 at Southwest Research Institute in San Antonio, TX
 The Laplace Transform & Some Combinatorial Identities  AMS Fall Sectional Meeting*  10/03/15 at Loyola University in Chicago, IL
 ShiftEquivalence in Consecutive Pattern Avoidance  Permutation Patterns  6/15/15 at the De Morgan House in London, England
 WilfEquivalence in Consecutive Patterns  University of Florida Combinatorics Seminar*  4/14/15 at the University of FL, Gainesville
 kEmbeddings and WilfEquivalence  Dartmouth College Combinatorics Seminar*  4/10/14 at Dartmouth College in Hanover, NH
Other Recent Talks
 Trinity University Majors' Seminar  3/23/2016  Slides
 Trinity University Majors' Seminar  3/18/2014  Slides
 Trinity University Majors' Seminar  2/17/2011  Slides
What Is My Erdös Number?
I'm often asked, by people when they first hear about this statistic, about my Erdös number, which is 3. The lineage is as follows:
 I wrote (many) a paper with Jeff Remmel who has an Erdös number of 2.
 Jeff Remmel wrote multiple papers with Henry (a.k.a. Hal) Kierstead who has an Erdös number of 1.
 Hal Kierstead wrote ``The Dimension of Random Ordered Sets" with Paul Erdös and W.T. Trotter in 1991. This paper was published in Random Structures Algorithms, 2, pages 253275.
Who Are My Mathematical Ancestors?
My thesis advisor was Jeff Remmel. To see who his advisor was, who his advisor's advisor was, etc., click
here and follow the links from advisor to advisor.
