Related papers: Descent polynomials for labeled tree

We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct…

We prove that the enumerative polynomials of quasi-Stirling permutations of multisets with respect to the statistics of plateaux, descents and ascents are partial $\gamma$-positive, thereby confirming a recent conjecture posed by Lin, Ma…

In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it.

We present an algorithmic mapping from permutations of length dn to labeled n-node d-ary trees and back again. Given such a bijection, one can interpret each of the factorials in the formula for the Catalan numbers as a count of…

It is known when we call a poset P, a $\mathcal{P}$-chain permutational poset, given a subset of permutations $\mathcal{P}$ of the symmetric group $S_{n}$. In this work, we use the same idea to study subsets of words of length $n$, that are…

We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree…

We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. In addition to divisibility and irreducibility results we also consider…

We present a decomposition of the generalized binomial coefficients associated with Jack polynomials into two factors: a stem, which is described explicitly in terms of hooks of the indexing partitions, and a leaf, which inherits various…

In mathematical phylogenetics, the time-consistent galled trees provide a simple class of rooted binary network structures that can be used to represent a variety of different biological phenomena. We study the enumerative combinatorics of…

The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…

In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.

We investigate the spectral properties of rooted trees with the intention of improving the currently existing results that deal with this matter. The concept of an assigned rational function is recursively defined for each vertex of a…

We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that…

We consider linear preferential attachment trees, and show that they can be regarded as random split trees in the sense of Devroye (1999), although with infinite potential branching. In particular, this applies to the random recursive tree…

For a labeled tree on the vertex set $\set{1,2,\ldots,n}$, the local direction of each edge $(i\,j)$ is from $i$ to $j$ if $i<j$. For a rooted tree, there is also a natural global direction of edges towards the root. The number of edges…

Here we consider the degenerate Bernstein polynomials as a degenerate version of Bernstein polynomials, which are motivated by Simsek's recent work 'Generating functions for unification of the multidimensional Bernstein polynomials and…

In this paper, we study the degenerate derangement polynomials and numbers, investigate some properties of those polynomials and numbers and explore their connections with the degenerate gamma distributions. In more detail, we derive their…

This paper is concerned with multivariate refinements of the gamma-positivity of Eulerian polynomials by using the succession and fixed point statistics. Properties of the enumerative polynomials for permutations, signed permutations and…

In this paper, we present an algorithm that enumerates a certain class of signed permutations, referred to as grid signed permutation classes. In the case of permutations, the corresponding grid classes are of interest because they are…

For a labelled tree on the vertex set $[n]:=\{1,2,..., n\}$, define the direction of each edge $ij$ to be $i\to j$ if $i<j$. The indegree sequence of $T$ can be considered as a partition $\lambda \vdash n-1$. The enumeration of trees with a…