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}
}
View PDF on arXiv
12 Citations
Background Citations
7
Methods Citations
3

Figures from this paper

12 Citations

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

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

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.

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

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

  • Bao-Xuan Zhu
  • Mathematics
    SIAM 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

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

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

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 $H_4$

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

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…

References

SHOWING 1-10 OF 52 REFERENCES

Lattice paths and branched continued fractions: An infinite sequence of generalizations of the Stieltjes--Rogers and Thron--Rogers polynomials, with coefficientwise Hankel-total positivity

We define an infinite sequence of generalizations, parametrized by an integer $m \ge 1$, of the Stieltjes--Rogers and Thron--Rogers polynomials; they arise as the power-series expansions of some…

Generalized Stirling permutations, families of increasing trees and urn models

Combinatorial aspects of continued fractions

On Path diagrams and Stirling permutations

The aim of this work is to introduce the notion of local types in $k-Stirling permutations, to relate these local types with nodes types in $(k+1)$-ary increasing trees and to obtain a bijection with suitably defined path diagrams.

Motzkin Paths, Motzkin Polynomials and Recurrence Relations

It is shown that the matrix entries of powers of an arbitrary tridiagonal matrix are essentially given by Motzkin polynomials, a property commonly known but usually stated without proof.

Combinatorial species and tree-like structures

The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labelled and unlabelled structures and as a tool for the…

Multivariate Fuss-Catalan numbers

  • J. Aval
  • Mathematics
    Discret. Math.
  • 2008

Totally Nonnegative Matrices

Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices,…

Total positivity of recursive matrices

Advanced Combinatorics: The Art of Finite and Infinite Expansions

I. Vocabulary of Combinatorial Analysis.- 1.1. Subsets of a Set Operations.- 1.2. Product Sets.- 1.3. Maps.- 1.4. Arrangements, Permutations.- 1.5. Combinations (without repetitions) or Blocks.- 1.6.…
...