Pétréolle, M;
Sokal, AD;
(2021)
Lattice paths and branched continued fractions II. Multivariate Lah polynomials and Lah symmetric functions.
European Journal of Combinatorics
, 92
, Article 103235. 10.1016/j.ejc.2020.103235.
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Abstract
We introduce the generic Lah polynomials Ln,k(ϕ), which enumerate unordered forests of increasing ordered trees with a weight ϕi for each vertex with i children. We show that, if the weight sequence ϕ is Toeplitz-totally positive, then the triangular array of generic Lah polynomials is totally positive and the sequence of row-generating polynomials Ln(ϕ,y) is coefficientwise Hankel-totally positive. Upon specialization we obtain results for the Lah symmetric functions and multivariate Lah polynomials of positive and negative type. The multivariate Lah polynomials of positive type are also given by a branched continued fraction. Our proofs use mainly the method of production matrices; the production matrix is obtained by a bijection from ordered forests of increasing ordered trees to labeled partial Łukasiewicz paths. We also give a second proof of the continued fraction using the Euler–Gauss recurrence method.
| Type: | Article |
|---|---|
| Title: | Lattice paths and branched continued fractions II. Multivariate Lah polynomials and Lah symmetric functions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.ejc.2020.103235 |
| Publisher version: | https://doi.org/10.1016/j.ejc.2020.103235 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10111699 |
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