Research

Publications

Update 8/17/15:  With changes to my old server, the webpages dedicated to each paper (which listed computer code, status of conjectures, slides from talks, etc.) have been temporarily disconnected.  This will get fixed in the near future.  Until then, email me for additional details.

(Reverse chronological order)

  1. Some Wilf-equivalences for vincular patterns.
    With Mark Shattuck.
    Journal of Combinatorics (Permutation Patterns 2013 special issue). Volume 6, no. 1-2, 19-45. (2015)
  2. Ascent sequences avoiding pairs of patterns.
    With Lara Pudwell
    Electronic Journal of Combinatorics. Volume 22, no. 1, Paper 1.58 (2015).
  3. Refining enumeration schemes to count according to permutation statistics.
    Electronic Journal of Combinatorics. Volume 21, Issue 2 (2014).  Presented at Permutation Patterns 2013.
  4. Shape-Wilf-equivalences for vincular patterns.
    Advances in Applied Mathematics. Volume 50, Number 5. 2013. Also available on ArXiv.org.
  5. Automatic generation of theorems and proofs on enumerating consecutive-Wilf classes.
    With Brian Nakamura and Doron Zeilberger.
    Presented at Waterloo Workshop in Computer Algebra 2011, W80
    Appeared in “Advances in Combinatorics: Waterloo Workshop in Computer Algebra, W80, May 26-29, 2011”, (edited by Ilias Kotsireas and Eugene Zima), 121-138.
  6. Enumeration schemes for vincular patterns.
    With Lara Pudwell.
    Discrete Mathematics. Volume 312 (10). 2012. 1699-1712.
  7. Pattern avoidance by even permutations.
    With Aaron D. Jaggard.
    Electronic Journal of Combinatorics. Volume 18(2). (2011).
  8. Algorithms for Permutation Statistics
    Ph.D. Thesis. May 2011.
  9. The number of inversions and the major index of permutations are asymptotically joint-independently normal.
    With Doron Zeilberger.
    Personal Journal of Shalosh B. Ekhad and Doron Zeilberger. February 2011.
  10. Refining enumeration schemes to count according to the inversion number.
    Pure Mathematics and Applications. Volume 21. Issue No. 2. (2010).
  11. Applying the cluster method to count occurences of generalized permutation patterns.
    Difference Equations and Applications Vol. 17 (2011), no. 5, 709–720.
  12. Periodic orbits for billiards on an equilateral triangle.
    With Ron Umble.
    Amer. Math. Monthly Vol. 115 (2008), no. 6, 479–491.

Upcoming

  • Enumeration schemes for pattern-avoiding ascent sequences.  With Lara Pudwell.  In preparation.
  • Peak-Wilf-Equivalence.  With Charles Walker.  In preparation.

Undergraduate Research

I have mentored undergraduate research projects with the following students.

  • Charles Walker.  PSU.  Summer 2013.
  • Ross Nycum. PSU. Spring 2013.
  • Jonathan Eskreis-Winkler. Rutgers REU. Summer 2011.
  • Ethan McCarthy. Rutgers REU. Summer 2011.

Numbers

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