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math.CO2026
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…
math.CO2026
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…
math.CO2026
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…