1 citations · 1 across the 9 of their papers we have counts for
10 papers
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…
A Combinatorial Framework for the Pons-Batle Identity: Young Tableaux, Lattice Paths, and Limit Laws
Hexuan Liu, Michael Wallner, Guan-Ru Yu
Tree-child networks are an important class of phylogenetic network used to model reticulate evolutionary processes. These networks have attracted increasing attention from research…
The decompressed tree size of -ary chains
Michael Wallner
A chain is defined as a directed acyclic graph (DAG) with one source and one sink, where the children are ordered and the spanning tree computed using a depth-first search is a pat…
Bivariate asymptotics via random walks: application to large genus maps
Andrew Elvey Price, Wenjie Fang, Baptiste Louf +1
We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two r…
Bijections between Variants of Dyck Paths and Integer Compositions
Manosij Ghosh Dastidar, Michael Wallner
We give bijective results between several variants of lattice paths of length (or ) and integer compositions of n, all enumerated by the seemingly innocuous formula $4^{…
A Bijection between Stacked Directed Polyominoes and Motzkin Paths with Alternative Catastrophes
Florian Schager, Michael Wallner
We present a novel bijection between stacked directed polyominoes and Motzkin paths with catastrophes. Further, we leverage this new bridge between these two worlds to obtain a bet…
Asymptotics of relaxed -ary trees
Manosij Ghosh Dastidar, Michael Wallner
A relaxed -ary tree is an ordered directed acyclic graph with a unique source and sink in which every node has out-degree . These objects arise in the compression of trees in…
Bijections and congruences involving lattice paths and integer compositions
Manosij Ghosh Dastidar, Michael Wallner
We prove new bijections between different variants of Dyck paths and integer compositions, which give combinatorial explanations of their simple counting formula . These g…
Composition schemes: q-enumerations and phase transitions
Cyril Banderier, Markus Kuba, Stephan Wagner +1
Composition schemes are ubiquitous in combinatorics, statistical mechanics and probability theory. We give a unifying explanation to various phenomena observed in the combinatorial…
Combinatorics of nondeterministic walks
Élie de Panafieu, Michael Wallner
This paper introduces nondeterministic walks, a new variant of one-dimensional discrete walks. The main difference to classical walks is that its nondeterministic steps consist of…