AEC logo 5th Algorithmic and Enumerative Combinatorics
Summer School 2019

Invited Speakers

  • Nicolas Broutin (Sorbonne Université, France)

  • George Labahn (University of Waterloo, Canada)

    Order Bases : Applications and Computation
    Abstract: Order Bases takes as input a vector or matrix of power series F and describes all solutions (as a module) for approximation problems of the form F p = O(zω) with ω a scalar or a vector. These approximation problems date back to the work of Hermite and his student Padé and later contributions for Order bases were given by Mahler. More recently applications of Order bases to problems in Combinatorics have appeared through the work of Salvy and Bostan. In these lectures we give the history (basically coming from rational approximation and interpolation problems), fast algorithms for computation and applications. The applications will include fast computation of problems with matrix polynomial arithmetic, matrix normal forms in addition to the problems arising in Combinatorics.

  • Alan Sokal (University College London, U.K. and New York University, U.S.A.)

    Continued fractions and Hankel-total positivity