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Hankel Determinants of convoluted Catalan numbers and nonintersecting lattice paths: A bijective proof of Cigler's Conjecture (2402.19127v2)
Published 29 Feb 2024 in math.CO
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 Lindstr\"om-Gessel-Viennot-method and a certain construction involving reflections and overlays of nonintersecting lattice paths. Shortly after this bijective proof was presented here, Cigler provided a shorter proof based on earlier results.