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 10/15/2012.

My Publications

• ``Minimal Overlapping Embeddings & Exact Matches in Words"
  • Submitted, October of 2011
  • Co-author: J. Remmel
• ``Two q-Analogues of Poly-Stirling Numbers" .pdf, .ps
  • 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, .ps
  • Journal of Integer Sequences 13 (2010), 10.3.3
• ``Augmented Rook Boards & General Product Formulas" .pdf, .ps
  • Electronic Journal of Combinatorics 15 (2008), R85
  • Co-author: J. Remmel
• ``Connection Coeffcients Between Rising & Falling Factorial Bases"
  • In Preparation
  • Co-authors: J. Liese & J. Remmel

My Recent Research Talks (* = invited talk)

• AMS Sectional Meeting* - 10/13/12 at Tulane University in New Orleans, LA - Slides

• Permutation Patterns - 06/14/12 at Strathclyde University in Glasgow, Scotland - Slides

• CombinaTexas - 04/21/12 at Southwestern Univeristy in Georgetown, TX - Slides

• Permutation Patterns - 06/24/2011 at Cal Poly in San Luis Obispo, CA - Slides

Other Talks

• Trinity University Majors' Seminar - 02/17/2011 - Slides

• JMM Projext NExT Capstone Panel - 01/16/2010 - Slides

What Is My Erdös Number?

Because I always get asked this by students who hear about Paul Erdös and get interested in this sort of thing, I did a little poking around and found that my Erdös number is 3. The lineage is as follows:

         - I have written a paper with Jeff Remmel who has an Erdös number of 2.

         - Jeff Remmel has written 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?

As stated above, my thesis advisor is Jeff Remmel. To see who his advisor was, and who his advisor's advisor was, and so on, click here and follow the links from advisor to advisor. (This link is brought to you by the Mathematics Geneology Project run out of NDSU.)