8 papers
Growing Binary Trees
Olivier Bodini, Antoine Genitrini, Khaydar Nurligareev
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction…
Asymptotic probability of irreducibles III: Anti-SEQ
Thierry Monteil, Khaydar Nurligareev
In this paper, we study the structure of the complete asymptotic expansion of the probability that a large combinatorial object is connected or consists of a given number of connec…
Brick Wall Excursions: Combinatorial Interpretation of Random Flight Moments
Sergey Kirgizov, Khaydar Nurligareev, Michael Wallner
We study the expected distance of short uniform random walks in arbitrary dimensions with unit steps in random directions. It is known that for dimensions and , all the…
The Distribution of the Deepest Leaves in Binary Trees
Olivier Bodini, Antoine Genitrini, Khaydar Nurligareev
We study the extreme local structure of plane binary trees through the distribution of leaves at maximum depth. We first address two basic questions: (i) the asymptotic probability…
Asymptotic probability of irreducibles II: sequence
Thierry Monteil, Khaydar Nurligareev
This paper is devoted to the structure of the complete asymptotic expansion of the probability that a large combinatorial object is irreducible or consists of a given number of irr…
Endhered patterns in matchings and RNA
Célia Biane, Greg Hampikian, Sergey Kirgizov +1
An endhered (end-adhered) pattern is a subset of arcs in matchings, such that the corresponding starting points are consecutive and the same holds for the ending points. Such patte…