4 papers · 1 filter
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…