4 papers
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 . For complete graphs , we give a new proof of the fact, originally obtained by M…
Boolean-Narayana numbers
Miklos Bona
We introduce a refinement of Boolean-Catalan numbers and call them Boolean-Narayana numbers. We provide an explicit formula for these numbers, and prove unimodality, log-concavity,…
Counting pairs of cycles whose product is a permutation with restricted cycle lengths
Miklos Bona, Boris Pittel
We find exact and asymptotic formulas for the number of pairs of -cycles such that the all cycles of the product have lengths from a given integer set. We the…
The likely maximum size of twin subtrees in a large random tree
Miklos Bona, Ovidiu Costin, Boris Pittel
We call a pair of vertex-disjoint, induced subtrees of a rooted trees twins if they have the same counts of vertices by out-degrees. The likely maximum size of twins in a uniformly…