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 & Poly-Stirling Numbers

Thesis Advisor: Dr. Jeff Remmel , UC, San Diego

My CV

My CV as of 11/30/2024.

My Publications

• ``Two combinatorial interpretations of rascal numbers" -- .pdf
  • Journal of Integer Sequences 27 (2024), 24.8.2
  • Co-author: A. Gibbs (TU student, Class of 2025)
• ``Improving foresight predictions in the 2002–2018 NFL regular-seasons: A classic tale of quantity vs. quality" -- .pdf
  • Journal of Advances in Mathematics and Computer Science 34(1-2) (2019) : DOI
  • Co-author: E. C. Balreira
• ``Shift equivalence in the generalized factor order" -- arXiv pdf
  • Archiv der Mathematik (2018): DOI
  • Co-authors: 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
  • Co-authors: 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
  • Co-authors: 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
  • Co-authors: 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
  • Co-author: J. Remmel
• ``Two q-Analogues of Poly-Stirling 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
• ``m-Partition Boards & Poly-Stirling 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
  • Co-author: J. Remmel

Some Recent Research Talks (* = invited talk)

• A,B-Minimal 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

• Shift-Equivalence in Consecutive Pattern Avoidance - Permutation Patterns - 6/15/15 at the De Morgan House in London, England

• Wilf-Equivalence in Consecutive Patterns - University of Florida Combinatorics Seminar* - 4/14/15 at the University of FL, Gainesville

• k-Embeddings and Wilf-Equivalence - Dartmouth College Combinatorics Seminar* - 4/10/14 at Dartmouth College in Hanover, NH

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 253-275.

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.