14 citations · 87 across the 22 of their papers we have counts for
6 papers · 1 filter
Divisibility of binomial coefficients by powers of two
Lukas Spiegelhofer, Michael Wallner
For nonnegative integers and let be the number of entries in the -th row of Pascal's triangle that are not divisible by . In this paper we prove that t…
The Tu--Deng Conjecture holds almost surely
Lukas Spiegelhofer, Michael Wallner
The Tu--Deng Conjecture is concerned with the sum of digits of in base~ (the Hamming weight of the binary expansion of ) and states the following: assume that …
On the shape of random Pólya structures
Bernhard Gittenberger, Emma Yu Jin, Michael Wallner
Panagiotou and Stufler recently proved an important fact on their way to establish the scaling limits of random Pólya trees: a uniform random Pólya tree of size consists of a c…
Lattice paths with catastrophes
Cyril Banderier, Michael Wallner
In queuing theory, it is usual to have some models with a "reset" of the queue. In terms of lattice paths, it is like having the possibility of jumping from any altitude to zero. T…
A bijection of plane increasing trees with relaxed binary trees of right height at most one
Michael Wallner
Plane increasing trees are rooted labeled trees embedded into the plane such that the sequence of labels is increasing on any branch starting at the root. Relaxed binary trees are…
Asymptotic Enumeration of Compacted Binary Trees of Bounded Right Height
Antoine Genitrini, Bernhard Gittenberger, Manuel Kauers +1
A compacted binary tree is a graph created from a binary tree such that repeatedly occurring subtrees in the original tree are represented by pointers to existing ones, and hence e…