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Seminar on Complex Analysis (Gonchar Seminar)
January 22, 2024 17:00–19:00, Moscow, Steklov Institute, room 110
 


On a generalisation of the Laguerre polynomials

A. V. Dyachenko

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow

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Abstract: Foata and Strehl found a beautiful combinatorial interpretation of the Laguerre polynomials: it turns out that these polynomials count the so-called Laguerre digraphs generalising digraphs of cyclic permutations. During my talk, I would like to introduce a multivariate generalisation of the Laguerre polynomials related to such graphs, as well as certain properties of matrices built from sequences of such polynomials. In particular, I will state conditions implying total nonnegativity (i.e. nonnegativity of all minors) of such matrices.

Website: https://zoom.us/j/7743848073?pwd=QnJmZjQ5OEV1c3pjenBhcUMwWW9XUT09

References
  1. Bishal Deb, Alexander Dyachenko, Mathias Pétréolle, Alan D. Sokal, Lattice paths and branched continued fractions. III. Generalizations of the Laguerre, rook and Lah polynomials, 2023 finalinfo arXiv: arXiv-paper; 2312.1108


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