Hankel determinants of convoluted Catalan numbers and nonintersecting lattice paths: A bijective proof of Cigler's conjecture
Year: 2025
Type: article
Abstract: In recent preprints, Cigler considered certain Hankel determinants of convoluted Catalan numbers and conjectured identities for these determinants.In this note, we shall give a bijective proof of Cigler's Conjecture by interpreting determinants as generating functions of nonintersecting lattice paths: this proof employs the reflection principle, the Lindström-Gessel-Viennot-method, and a certain construction involving reflections and overlays of nonintersecting lattice paths.Shortly after the bijective proof was presented here, Cigler provided a shorter proof based on earlier results.
Author: Markus Fulmek
Institution: University of Vienna
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409543175