25 citations · 43 across the 9 of their papers we have counts for
10 papers
The inverse problem for the Steiner-Wiener index of trees
Adrian Beker, Rudi Mrazović
For a connected graph and a set , the Steiner distance is the minimum number of edges in a connected subgraph of containing . The Steiner-Wiener…
A note on the shortest law for the symmetric group
Adrian Beker, Luka Milićević, Rudi Mrazović
Let denote the length of the shortest non-trivial two-variable law for the symmetric group . Buskin's quantitative subgroup-separability argument gives the classical lo…
Lines in the prime number graph
Scott Duke Kominers, Rudi Mrazović, Carl Pomerance +1
The prime number graph is the set of points where denotes the prime. Let be the minimum number of straight line segments needed to cover the fir…
Expected perimeter and area of the convex hull of planar Brownian motion stopped upon exiting the unit disk
Rudi Mrazović, Hugo Panzo, Stjepan Šebek
We study the convex hull of planar Brownian motion run until the exit time from the unit disk. Our primary objectives are to compute the expected perimeter and expected area of thi…
Equidistribution of Diophantine pairs among the equivalence classes of quadratic forms
Goran Dražić, Matija Kazalicki, Rudi Mrazović
For a fixed integer n, a pair of nonzero integers {a, c} is called a D(n)-pair if the product ac plus n is a perfect square. In this short note we prove that D(n)-pairs are asympto…
Transversals in quasirandom latin squares
Sean Eberhard, Freddie Manners, Rudi Mrazović
A transversal in an latin square is a collection of entries not repeating any row, column, or symbol. Kwan showed that almost every latin square has $…
Capacity of the range of random walks on groups
Rudi Mrazović, Nikola Sandrić, Stjepan Šebek
In this paper, we discuss asymptotic behavior of the capacity of the range of symmetric simple random walks on finitely generated groups. We show the corresponding strong law of la…
An asymptotic for the Hall--Paige conjecture
Sean Eberhard, Freddie Manners, Rudi Mrazović
Hall and Paige conjectured in 1955 that a finite group has a complete mapping if and only if its Sylow -subgroups are trivial or noncyclic. This conjecture was proved in 200…
A random model for the Paley graph
Rudi Mrazović
For a prime we define the Paley graph to be the graph with the set of vertices , and with edges connecting vertices whose sum is a quadratic residue. Pa…
Additive triples of bijections, or the toroidal semiqueens problem
Sean Eberhard, Freddie Manners, Rudi Mrazović
We prove an asymptotic for the number of additive triples of bijections , that is, the number of pairs of bijections $π_1,π_2\colon \{1,\dot…