University of Klagenfurt

output

19992026

most citedCellular-Connected UAVs over 5G: Deep Reinforcement Learning for Interference Management

464 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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38 papers · 1 filter

math.CO2025

Patterns in rectangulations. Part I: $⊤$ -like patterns, inversion sequence classes $I (010, 101, 120, 201)$ and $I (011, 201)$ , and rushed Dyck paths

Andrei Asinowski, Michaela A. Polley

We initiate a systematic study of pattern avoidance in rectangulations. We give a formal definition of such patterns and investigate rectangulations that avoid $⊤$ -like patterns…

math.CO2024

Characterization of Trees with Maximum Security

Alex S. A. Alochukwu, Audace A. V. Dossou-Olory, Fadekemi J. Osaye +5

The rank (also known as protection number or leaf-height) of a vertex in a rooted tree is the minimum distance between the vertex and any of its leaf descendants. We consider the s…

math.CO2024

Analysis of Regular Sequences: Summatory Functions and Divide-and-Conquer Recurrences

Clemens Heuberger, Daniel Krenn, Tobias Lechner

In the asymptotic analysis of regular sequences as defined by Allouche and Shallit, it is usually advisable to study their summatory function because the original sequence has a to…

math.CO2023

The distribution of the maximum protection number in simply generated trees

Clemens Heuberger, Sarah J. Selkirk, Stephan Wagner

The protection number of a vertex $v$ in a tree is the length of the shortest path from $v$ to any leaf contained in the maximal subtree where $v$ is the root. In this paper, we de…

math.CO2022★ 2 cited

Enumeration of Generalized Dyck Paths Based on the Height of Down-Steps Modulo $k$

Clemens Heuberger, Sarah J. Selkirk, Stephan Wagner

For fixed non-negative integers $k$ , $t$ , and $n$ , with $t < k$ , a $k_{t}$ -Dyck path of length $(k + 1) n$ is a lattice path that starts at $(0, 0)$ , ends at $((k + 1) n, 0)$ , stays weakly…

math.CO2022

A Note on the Relation between Recognisable Series and Regular Sequences, and their Minimal Linear Representations

Clemens Heuberger, Daniel Krenn, Gabriel F. Lipnik

In this note, we precisely elaborate the connection between recognisable series (in the sense of Berstel and Reutenauer) and $q$ -regular sequences (in the sense of Allouche and Sha…

math.CO2021

Sum-of-Squares Certificates for Vizing's Conjecture via Determining Gröbner Bases

Elisabeth Gaar, Melanie Siebenhofer

The famous open Vizing conjecture claims that the domination number of the Cartesian product graph of two graphs $G$ and $H$ is at least the product of the domination numbers of $G…

math.CO2021★ 6 cited

Asymptotic Analysis of q-Recursive Sequences

Clemens Heuberger, Daniel Krenn, Gabriel F. Lipnik

For an integer $q \geq 2$ , a $q$ -recursive sequence is defined by recurrence relations on subsequences of indices modulo some powers of~ $q$ . In this article, $q$ -recursive sequences a…

math.CO2020★ 4 cited

Down-step statistics in generalized Dyck paths

Andrei Asinowski, Benjamin Hackl, Sarah J. Selkirk

The number of down-steps between pairs of up-steps in $k_{t}$ -Dyck paths, a generalization of Dyck paths consisting of steps ${(1, k), (1, - 1)}$ such that the path stays (weakly) a…

math.CO2020★ 2 cited

Towards a Computational Proof of Vizing's Conjecture using Semidefinite Programming and Sums-of-Squares

Elisabeth Gaar, Daniel Krenn, Susan Margulies +1

Vizing's conjecture (open since 1968) relates the product of the domination numbers of two graphs to the domination number of their Cartesian product graph. In this paper, we formu…

math.CO2020★ 5 cited

Flip-sort and combinatorial aspects of pop-stack sorting

Andrei Asinowski, Cyril Banderier, Benjamin Hackl

Flip-sort is a natural sorting procedure which raises fascinating combinatorial questions. It finds its roots in the seminal work of Knuth on stack-based sorting algorithms and lea…

math.CO2019★ 6 cited

Monotonic Representations of Outerplanar Graphs as Edge Intersection Graphs of Paths on a Grid

Eranda Cela, Elisabeth Gaar

In a representation of a graph $G$ as an edge intersection graph of paths on a grid (EPG) every vertex of $G$ is represented by a path on a grid and two paths share a grid edge iff…

math.CO2019★ 1 cited

A Combinatorial Identity for Rooted Labeled Forests

Benjamin Hackl

In this brief note a straightforward combinatorial proof for an identity directly connecting rooted forests and unordered set partitions is provided. Furthermore, references that p…

math.CO2019

Algorithmic counting of nonequivalent compact Huffman codes

Christian Elsholtz, Clemens Heuberger, Daniel Krenn

It is known that the following five counting problems lead to the same integer sequence~ $f_{t} (n)$ : the number of nonequivalent compact Huffman codes of length~ $n$ over an alphabet o…

math.CO2019★ 2 cited

An Optimization-Based Sum-of-Squares Approach to Vizing's Conjecture

Elisabeth Gaar, Daniel Krenn, Susan Margulies +1

Vizing's conjecture (open since 1968) relates the sizes of dominating sets in two graphs to the size of a dominating set in their Cartesian product graph. In this paper, we formula…

math.CO2018★ 6 cited

Asymptotic Analysis of Regular Sequences

Clemens Heuberger, Daniel Krenn

In this article, $q$ -regular sequences in the sense of Allouche and Shallit are analysed asymptotically. It is shown that the summatory function of a regular sequence can asymptoti…

math.CO2018★ 1 cited

Esthetic Numbers and Lifting Restrictions on the Analysis of Summatory Functions of Regular Sequences

Clemens Heuberger, Daniel Krenn

When asymptotically analysing the summatory function of a $q$ -regular sequence in the sense of Allouche and Shallit, the eigenvalues of the sum of matrices of the linear representa…

math.CO2018★ 1 cited

Analysis of Summatory Functions of Regular Sequences: Transducer and Pascal's Rhombus

Clemens Heuberger, Daniel Krenn, Helmut Prodinger

The summatory function of a $q$ -regular sequence in the sense of Allouche and Shallit is analysed asymptotically. The result is a sum of periodic fluctuations for eigenvalues of ab…

math.CO2018★ 4 cited

Ascents in Non-Negative Lattice Paths

Benjamin Hackl, Clemens Heuberger, Helmut Prodinger

Non-negative Łukasiewicz paths are special two-dimensional lattice paths never passing below their starting altitude which have only one single special type of down step. They are…

math.CO2017★ 2 cited

Fringe Analysis of Plane Trees Related to Cutting and Pruning

Benjamin Hackl, Clemens Heuberger, Sara Kropf +1

Rooted plane trees are reduced by four different operations on the fringe. The number of surviving nodes after reducing the tree repeatedly for a fixed number of times is asymptoti…

math.CO2017

Growing and Destroying Catalan-Stanley Trees

Benjamin Hackl, Helmut Prodinger

Stanley lists the class of Dyck paths where all returns to the axis are of odd length as one of the many objects enumerated by (shifted) Catalan numbers. By the standard bijection…

math.CO2017★ 8 cited

Protection Number in Plane Trees

Clemens Heuberger, Helmut Prodinger

The protection number of a plane tree is the minimal distance of the root to a leaf; this definition carries over to an arbitrary node in a plane tree by considering the maximal su…

math.CO2016★ 3 cited

Reductions of Binary Trees and Lattice Paths induced by the Register Function