# Lattice paths and branched continued fractions II. Multivariate Lah polynomials and Lah symmetric functions

@article{Ptrolle2019LatticePA, title={Lattice paths and branched continued fractions II. Multivariate Lah polynomials and Lah symmetric functions}, author={Mathias P{\'e}tr{\'e}olle and Alan D. Sokal}, journal={Eur. J. Comb.}, year={2019}, volume={92}, pages={103235} }

## 12 Citations

### Lattice paths, vector continued fractions, and resolvents of banded Hessenberg operators

- Mathematics
- 2022

We give a combinatorial interpretation of vector continued fractions obtained by applying the Jacobi-Perron algorithm to a vector of p ≥ 1 resolvent functions of a banded Hessenberg operator of order…

### Multiple orthogonal polynomials associated with branched continued fractions for ratios of hypergeometric series

- Mathematics
- 2022

The main objects of the investigation presented in this paper are branched-continued-fraction representations of ratios of contiguous hypergeometric series and type II multiple orthogonal polynomials…

### Total positivity from a generalized cycle index polynomial.

- Mathematics
- 2020

Log-concavity and almost log-convexity of the cycle index polynomials were proved by Bender and Canfield [J. Combin. Theory Ser. A 74 (1996)]. Schirmacher [J. Combin. Theory Ser. A 85 (1999)]…

### Coefficientwise Hankel-total positivity of row-generating polynomials for the $m$-Jacobi-Rogers triangle

- Mathematics
- 2022

Total positivity of matrices is deeply studied and plays an important role in various branches of mathematics. Recently, based on lattice paths and branched continued fractions, Pétréolle, Sokal and…

### Total Positivity from the Exponential Riordan Arrays

- MathematicsSIAM Journal on Discrete Mathematics
- 2021

Log-concavity and almost log-convexity of the cycle index polynomials were proved by Bender and Canfield [J. Combin. Theory Ser. A 74 (1996)]. Schirmacher [J. Combin. Theory Ser. A 85 (1999)]…

### Trees, Forests, and Total Positivity: I. $q$-Trees and $q$-Forests Matrices

- MathematicsThe Electronic Journal of Combinatorics
- 2021

We consider matrices with entries that are polynomials in $q$ arising from natural $q$-generalisations of two well-known formulas that count: forests on $n$ vertices with $k$ components; and rooted…

### THE e-POSITIVITY OF MULTIVARIATE kORDER EULERIAN POLYNOMIALS

- Mathematics
- 2021

Inspired by the recent work of Chen and Fu on the e-positivity of trivariate secondorder Eulerian polynomials, we show the e-positivity of a family of multivariate k-th order Eulerian polynomials. A…

### Combinatorial properties of multidimensional continued fractions

- Mathematics
- 2022

The study of combinatorial properties of mathematical objects is a very important research ﬁeld and continued fractions have been deeply studied in this sense. However, multidimensional continued…

### Three- and four-term recurrence relations for Horn's hypergeometric function $H_4$

- MathematicsResearches in Mathematics
- 2022

Three- and four-term recurrence relations for hypergeometric functions of the second order (such as hypergeometric functions of Appell, Horn, etc.) are the starting point for constructing branched…

### Multiple orthogonal polynomials, $d$-orthogonal polynomials, production matrices, and branched continued fractions

- Mathematics
- 2022

I analyze an unexpected connection between multiple orthogonal polynomials, d -orthogonal polynomials, production matrices and branched continued fractions. This work can be viewed as a partial…

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