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math.CO2026
The Partition Pairing Theorems I
George Andrews, Manosij Ghosh Dastidar
The aim of this paper is to introduce pairing theory for partitions. We begin with two statistics on integer partitions, the \emph{pairing index} and the \emph{pairing rank}. The p…
math.CO2024
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^{…
math.CO2024
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…