Eric S. Egge

Professor of Mathematics

I am originally from Park Rapids, Minnesota, a small resort town in the lake country of central Minnesota. I did my undergraduate work in Mathematics at Carleton College in Northfield, Minnesota. I did my graduate work in Mathematics at the University of Wisconsin-Madison, under the direction of Paul Terwilliger. I earned my Ph. D. in Mathematics in May of 2000 and then spent five years as an Assistant Professor of Mathematics at Gettysburg College. I returned to Carleton in the fall of 2005, as an Assistant Professor of Mathematics, I was promoted to Associate Professor of Mathematics in the fall of 2009, and I was promoted to Professor of Mathematics in the fall of 2015.

My mathematical interests are in algebra and combinatorics, especially enumerative and algebraic combinatorics. My research includes work on pattern-avoiding permutations, a generalization of the Terwilliger algebra of a distance-regular graph or association scheme, the combinatorics of symmetric functions, and the combinatorics of the Legendre-Stirling and Jacobi-Stirling numbers. I am also interested in undergraduate problem-solving, undergraduate research, and games and puzzles with mathematical connections. In my spare time I enjoy reading, writing, running, baking pizza, cheesecake, cookies, and brownies, and playing games with my family.

Each electronic version below is my copy of the final version of the listed paper. To obtain a copy of the published version of any paper for which an electronic version is listed, please contact me directly.
  • Tilings of Aztec Diamonds, Baxter Permutations, and Snow Leopard Permutations, with Ben Caffrey, Greg Michel, Kailee Rubin, and Jon Ver Steegh, submitted, preprint.

  • The Jacobi-Stirling Numbers, with George E. Andrews, Wolfgang Gawronski, and Lance L. Littlejohn, Journal of Combinatorial Theory, Series A, vol. 120, pp. 288-303, 2013, preprint on arXiv.

  • From Quasisymmetric Expansions to Schur Expansions via a Modified Inverse Kostka Matrix, with Nicholas A. Loehr and Gregory S. Warrington, European Journal of Combinatorics, vol. 31, pp. 2014-2027, 2010, electronic version.

  • Legendre-Stirling Permutations, European Journal of Combinatorics, vol. 31, pp. 1735-1750, 2010, electronic version.

  • Enumerating rc-Invariant Permutations with No Long Decreasing Subsequences, Annals of Combinatorics, vol. 14, pp. 85-101, 2010, electronic version.

  • The Pfaffian Transform, with Tracale Austin, Hans Bantilan, Isao Jonas, and Paul Kory, Journal of Integer Sequences, vol. 12, Article 09.1.5, 2009, published version.

  • Restricted Symmetric Permutations, Annals of Combinatorics, vol. 11, pp. 405-434, 2007, electronic version.

  • Restricted Colored Permutations and Chebyshev Polynomials, Discrete Mathematics, vol. 307, pp. 1792-1800, 2007, electronic version.

  • Restricted Signed Permutations Counted by the Schroder Numbers, Discrete Mathematics, vol. 306, pp. 552-563, 2006, electronic version.

  • Bivariate Generating Functions for Involutions Restricted by 3412, with Toufik Mansour, Advances in Applied Mathematics, vol. 36, pp. 118-137, 2006, electronic version.

  • Restricted Permutations, Fibonacci Numbers, and k-Generalized Fibonacci Numbers, with Toufik Mansour, Integers: The Electronic Journal of Combinatorial Number Theory, vol. 5, article A1, 2005, online version.

  • 231-Avoiding Involutions and Fibonacci Numbers, with Toufik Mansour, Australasian Journal of Combinatorics, vol. 30, pp. 75--84, 2004, electronic version.

  • Restricted 3412-Avoiding Involutions, Continued Fractions, and Chebyshev Polynomials, Advances in Applied Mathematics, vol. 33, pp. 451-475, 2004, electronic version.

  • 132-Avoiding Two-stack Sortable Permutations, Fibonacci Numbers, and Pell Numbers, with Toufik Mansour, Discrete Applied Mathematics, vol. 143, pp. 72-83, 2004, electronic version.

  • A Schroder Generalization of Haglund's Statistic on Catalan Paths, with James Haglund, Kendra Killpatrick, and Darla Kremer, Electronic Journal of Combinatorics, vol. 10, article #R16, 2003, online version.

  • Permutations Which Avoid 1243 and 2143, Continued Fractions, and Chebyshev Polynomials, with Toufik Mansour, Electronic Journal of Combinatorics, vol. 9(2), article #R7, 2003, online version.

  • A Weight-Preserving Bijection Between Schroder Paths and Schroder Permutations, with Jason Bandlow and Kendra Killpatrick, Annals of Combinatorics, vol. 6, pp. 235-248, 2002, electronic version.

  • The Generalized Terwilliger Algebra and its Finite Dimensional Modules when d=2, Journal of Algebra, vol. 250, pp. 178-216, 2002, electronic version.

  • A Generalization of the Terwilliger Algebra, Journal of Algebra, vol. 233, pp. 213-252, 2000, electronic version.
Here are links to the slides for some of my recent talks. It's possible some of these slides will not display correctly on some browsers. If you notice a problem like this, please email me and I will try to correct it.

  • A Chromatic Symmetric Function for Signed Graphs, AMS Special Session on Combinatorics of Symmetric Functions, Athens, GA, March 5, 2016, slides.

  • A New Notion of Noncontiguous Containment for Ordered, Rooted Trees, AMS Special Session on Enumerative Combinatorics and Graph Theoretic Applications, Chicago, IL, October 4, 2015, slides.

  • Snow Leopard Permutations, Even Knots, Odd Knots, Janus Knots, and Restricted Catalan Paths, Midwest Combinatorics Conference, Minneapolis, MN, May 21, 2015, slides.

  • Catalan Combinatorics of Borel Ideals and Generalizations, AMS Special Session on Algebraic Combinatorics, Eau Claire, WI, September 21, 2014, slides.

  • Introducing 05A06: Patterns in Permutations in Words, AMS Special Session on Patterns in Permutations and Words, and Applications, Eau Claire, WI, September 20, 2014, slides.

  • New Pattern-Avoiding Permutations Counted by the Schroder Numbers, AMS Special Session on Permutation Patterns, Algorithms, and Enumerative Combinatorics, Rochester, NY, September 23, 2012, slides.

  • Pattern-Avoiding Permutations and Lattice Paths: Old Connections and New Links, MAA Mathfest Invited Paper Session Walk the Walk, Talk the Talk, Madison, WI, August 3, 2012, slides.

  • Linear Recurrences and the Pfaffian Transform, MAA Mathfest Invited Paper Session on Combinatorics and Matrices, Madison, WI, August 2, 2012, slides.

  • The Jacobi-Stirling Numbers, AMS Special Session on Symmetric Functions, Quasisymmetric Functions, and Associated Combinatorics, George Washington University, Washington, DC, March 18, 2012, slides.

  • Symmetric Permutations with No Long Decreasing Subsequences, Joint Mathematics Meetings, AMS Session on Discrete Mathematics, San Francisco, CA, January 15, 2010, slides.

Here are several of the student projects I have supervised over the past eight years. Where possible, I have included links to papers in which the students wrote up their results. In other cases I have given a brief description of the project.

  • Mailing Address

    Department of Mathematics and Statistics
    Carleton College
    Northfield, MN 55057

  • Email Address

    eegge at-symbol (college name, eight letters) dot edu

  • Office

    CMC 223

  • Office Phone

    (507) 222-7623