3 citations · 7 across the 7 of their papers we have counts for
10 papers
Enumeration of rooted 3-connected bipartite planar maps
Marc Noy, Clément Requilé, Juanjo Rué
We provide the first solution to the problem of counting rooted 3-connected bipartite planar maps. Our starting point is the enumeration of bicoloured planar maps according to the…
Normal limiting distributions for systems of linear equations in random sets
Juanjo Rué, Maximilian Wötzel
We consider the binomial random set model where each element in is chosen independently with probability . We show that for essentially all regimes…
On the expected number of perfect matchings in cubic planar graphs
Marc Noy, Clément Requilé, Juanjo Rué
A well-known conjecture by Lovász and Plummer from the 1970s asserted that a bridgeless cubic graph has exponentially many perfect matchings. It was solved in the affirmative by Es…
Cycles of given lengths in unicyclic components in sparse random graphs
Marc Noy, Vonjy Rasendrahasina, Vlady Ravelomanana +1
Let be subset of and let be the number of cycles belonging to unicyclic components whose length is in in the random graph . We find…
On strong infinite Sidon and sets and random sets of integers
David Fabian, Juanjo Rué, Christoph Spiegel
A set of integers is an -strong Sidon set if the pairwise sums of its elements are far apart by a certain measure depending on , more specifically if $…
An Erdős--Fuchs Theorem for Ordered Representation Functions
Gonzalo Cao-Labora, Juanjo Rué, Christoph Spiegel
Let be a positive integer. We study concentration results for the ordered representation functions $r^{\leq}_k(A,n) = \# \big\{ (a_1 \leq \dots \leq a_k) \in A^k : a_1+\d…
Further results on random cubic planar graphs
Marc Noy, Clément Requilé, Juanjo Rué
We provide precise asymptotic estimates for the number of several classes of labelled cubic planar graphs, and we analyze properties of such random graphs under the uniform distrib…
The least common multiple of random sets of positive integers
Javier Cilleruelo, Juanjo Rué, Paulius Šarka +1
We study the typical behavior of the least common multiple of the elements of a random subset . For example we prove that $\text{lcm}\{a:\ a\in A\}=2^{n(1+…
On the error term of the logarithm of the lcm of a quadratic sequence
Juanjo Rué, Paulius Šarka, Ana Zumalacárregui
We study the logarithm of the least common multiple of the sequence of integers given by . Using a result of Homma on the distribution of roots of quadrati…
On dilates sums
Yahya Ould Hamidoune, Juanjo Rué
Let be a finite nonempty set of integers. An asymptotic estimate of several dilates sum size was obtained by Bukh. The unique known exact bound concerns the sum …