Fabian Burghart

collaborators

5 papers

math.CO2026

On the intersection of pairs of trees

Miklos Bona, Fabian Burghart, Stephan Wagner

We consider the number of common edges in two independent random spanning trees of a graph $G$ . For complete graphs $K_{n}$ , we give a new proof of the fact, originally obtained by M…

math.PR2026

Ancestries in random $d$ -DAGs

Fabian Burghart

We consider a random recursive DAG $G_{n}$ on the vertex set $[n]$ where every vertex $i \geq 2$ has out-degree $d$ , with the targets chosen uniformly at random among the earlier $i-1…

math.CO2026

On Cycles in Multiset Permutations, Parking Functions, and Related Structures

Calum Buchanan, Fabian Burghart, Stephan Wagner +1

In this paper we study cycles in multiset permutations and parking functions. As combinatorial objects, multiset permutations are essential building blocks for mappings and permuta…

math.CO2024

Polynomial invariants for rooted trees related to their random destruction

Fabian Burghart

We consider three bivariate polynomial invariants $P$ , $A$ , and $S$ for rooted trees, as well as a trivariate polynomial invariant $M$ . These invariants are motivated by random des…

math.CO2024

A bijection for the evolution of $B$ -trees

Fabian Burghart, Stephan Wagner

A $B$ -tree is a type of search tree where every node (except possibly for the root) contains between $m$ and $2 m$ keys for some positive integer $m$ , and all leaves have the same d…

On the intersection of pairs of trees

Ancestries in random d-DAGs

On Cycles in Multiset Permutations, Parking Functions, and Related Structures

Polynomial invariants for rooted trees related to their random destruction

A bijection for the evolution of B-trees

Ancestries in random $d$ -DAGs

A bijection for the evolution of $B$ -trees