Lattice paths enumerations weighted by ascent lengths
Jun Yan
TL;DR
This paper generalizes weighted enumeration problems for lattice paths based on ascent lengths, connecting them to parking functions, Catalan paths, and various combinatorial enumeration problems.
Contribution
It introduces a broad framework for weighted lattice path enumeration based on ascent lengths, extending previous work and linking to multiple combinatorial structures.
Findings
Derived new enumeration formulas for weighted lattice paths
Connected lattice path enumeration to parking functions and Catalan paths
Identified links with OEIS entries and other combinatorial problems
Abstract
Recent work of the author connected several parking function enumeration problems to enumerations of Catalan paths with respect to certain weight functions that are expressed in terms of the ascent lengths. Motivated by this, we generalise and solve analogous weighted enumeration problems for a large family of lattice paths and weight functions, and discuss their connections with other enumeration problems and OEIS entries.
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Taxonomy
TopicsAdvanced Graph Theory Research · graph theory and CDMA systems · Advanced Combinatorial Mathematics