Research Interests

 

Areas of interest: My main research interests lie in the area of enumerative and algebraic combinatorics, specifically in tableaux theory, symmetric function theory and the study of permutation statistics. 

Academic Research

  • The q-Kostka polynomials and the development of a combinatorial description for the q,t-Kostka polynomials.
  • The q-Schroder polynomials and the development of a combinatorial interpretation for a q,t-Schroder polynomial.
  • Permutation statistics and their relation to the q-Catalan and q-Schroder polynomials.
  • Fibonacci tableaux and the development of an evacuation procedure, a geometric construction, and a Hook Formula for these tableaux.
  • A combinatorial interpretation for Fibonacci Schur functions and a definition of a Littlewood-Richardson Rule for Fibonacci tableaux.

  • The effect of conceptual teaching on the skill development of students in Calculus 1 classes.
  • The effect of students' perceptions of their parents' attitudes towards math on students achievement in Algebra 1 classes.

 

Papers

  • "Recursions for the q-Kostka Polynomials", University of Minnesota Digital Dissertation Archives, 1998.  Link to UofM Library Archives.

  • Killpatrick, K.,  "A Combinatorial Proof of a Recursion for the q-Kostka Polynomials", Journal of Combinatorial Theory, Series A, 92 (2000), pgs. 29-53.  pdf file

  • Bandlow, J. and K. Killpatrick,  "An Area-to-Inv Bijections Between Dyck Paths and 312-Avoiding Permutations," Electronic Journal of Combinatorics, 8 (2001), no. 1., Paper 40, 16 pgs.  pdf file

  • Bandlow, J., E. Egge and K. Killpatrick, "A Weight-Preserving Bijection Between Schroder Paths and Pattern-Avoiding Schroder Permutations", Annals of Combinatorics, 6 (2002), pgs. 235-248.  pdf file

  • Chappell, K. and K. Killpatrick, "The effects of concept-based instruction on the conceptual understanding and skill development of Calculus students", PRIMUS, March 2003, Volume XIII, Number 1., pgs. 17-37.  PRIMUS website

  • Egge, E., J. Haglund, K. Killpatrick and D. Kremer, "A Schroder Generalization of Haglund's Statistic on Catalan Paths," Electronic Journal of Combinatorics, 10 (2003), no. 1., Paper R16, 21 pgs.  pdf file

  • Killpatrick, K., "Evacuation and a Geometric Construction for Fibonacci Tableaux", Journal of Combinatorial Theory, Series A, 110 (2005) 337-351.  pdf file

  • K. Killpatrick, "A Relationship Between the Major Index For Tableaux and the Charge Statistic For Permutations", Electronic Journal of Combinatorics, 12 (2005) No. 1, Paper 45.  pdf file

  • Iga, K. and K. Killpatrick, "Truck Drivers, a Straw, and Sharing a Glass of Water", College Math Journal, Vol. 37, No. 2, March 2006.  pdf file

  • N. Cameron and K. Killpatrick, "Domino Fibonacci Tableaux", Electronic Journal of Combinatorics, 13 (2006) No. 1, paper 45.  pdf file

  • S. Erbes, S. Hough, and K. Killpatrick, "Investigating Relationships Between Students' Attitudes Toward Mathematics, Perceived Parental Attitudes, Demographics and Achievement in Algebra",  in preparation.   Word file

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