Some bijections on set partitions

TL;DR

This paper aimed to establish bijections between certain set partitions but was withdrawn due to an error invalidating key proofs related to symmetry properties.

Contribution

The paper attempted to provide bijections on set partitions, specifically addressing symmetry between k-nonnesting and k-noncrossing partitions.

Findings

The proof of symmetry was invalidated by an error.

The paper was withdrawn and no valid results were published.

No new valid bijections or results are presented.

Abstract

This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).