Related papers: Some bijections on set partitions

The paper was withdrawn due to a gap in the proof of Lemma 3.

This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.

This paper has been withdrawn by the author, as the proof of Theorem 3.2 contains a flaw; subsequently, both it and Theorem 3.3 are not known to hold. The content of Section 5 has been improved and expanded upon in two separate papers. The…

This paper has been withdrawn by the author, due to a crucial error in the proof of Thm.1

Paper withdrawn, due a crucial error in the proof of Lemma 4.3: thus Theorems 1.2 and 1.3 remain unproven.

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.

This paper has been withdrawn by the author due to a critical error in the proof of Theorem A pointed out by Burkhard Wilking.

This paper has been withdrawn due a crucial mistake due to a crucial mistake in the proof of Lemma 2.3.

This paper is being withdrawn because an error was discovered in lemma 4.3. Although the rest of the paper appears to be correct, this error invalidates the proof of theorem 3.1 and theorem 3.3.

This paper has been withdrawn by the author due to a gap in the proof of Lemma 3.4

Set partitions avoiding $k$-crossing and $k$-nesting have been extensively studied from the aspects of both combinatorics and mathematical biology. By using the generating tree technique, the obstinate kernel method and Zeilberger's…

This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.

This paper is withdrawn. We found a mistake in Lemma 4.1

This paper has been withdrawn due to an error in the proof of Theorem 5.3.

This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.

This article has been withdrawn due to an error in a proof of the main result.

This paper is withdrawn because of an error in Lemma 3.1

In this note, we give a simple extension map from partitions of subsets of [n] to partitions of [n+1], which sends $\delta$-distant k-crossings to $(\delta+1)$-distant k-crossings (and similarly for nestings). This map provides a…

In this paper we show a a proof by explicit bijections of the famous Kirkman-Cayley formula for the number of dissections of a convex polygon. Our starting point is the bijective correspondence between the set of nested sets made by \(k\)…

This paper has been withdrawn by the author since the proof of Lemma 8 is not correct.