Related papers: Some bijections on set partitions
The total number of noncrossing partitions of type $\Psi$ is the $n$th Catalan number $\frac{1}{n+1}\binom{2n}{n}$ when $\Psi=A_{n-1}$, and the binomial $\binom{2n}{n}$ when $\Psi=B_n$, and these numbers coincide with the correspondent…
This paper has been withdrawn by the authors, due to the requirement of the Journal where a modified version will be published.
Due to a computational mistake this paper has been withdrawn.
This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).
This paper has been withdrawn by the authors due to essential errors in Theorem 5.6.
This paper has been withdrawn by the author due to incomplete interpretation for the results.
In this paper, we give a bijective proof of the reduced lecture hall partition theorem. It is possible to extend this bijection in lecture hall partition theorem. And refined versions of each theorems are also presented.
This paper has been withdrawn by the author due to a critical error in the proof of Theorem 5.4 on which the proof of the main theorem on the non-simplenss was based.
This paper has been withdrawn by the author due to a crucial error in equation (51).
We study a curious class of partitions, the parts of which obey an exceedingly strict congruence condition we refer to as "sequential congruence": the $m$th part is congruent to the $(m+1)$th part modulo $m$, with the smallest part…
In this paper, we present a generalization of one of the theorems in [G. E. Andrews, Partitions with parts separated by parity, \textit{Annals of Combinatorics} \textbf{23}(2019), 241 - 248], and give its bijective proof. Further variations…
This paper has been withdrawn by the author due to an error in the proof of Proposition 4.8.
This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.
This paper has been withdrawn by the authors. We have discovered an error in the evaluation of the diagram, which invalidates our conclusion.
We withdraw this paper due to insufficient arguments in the derivation of Theorem 1. See quant-ph/0005062 for the new paper
This paper has been withdrawn by the author due to a errors in figure 3,4
This paper has been withdrawn by the authors, due to an error in the proof of Lemma 3.1.
In this note a bijection is constructed between the set of partitions of n simultaneously s-regular and t-distinct, and those simultaneously t-regular and s-distinct. Some implications of the map are discussed. As a generalized version of…
This paper has been withdrawn due to non-clearness of some technical points, as well as lack of a reasonable statement of quantization conjecture.
This paper has been withdrawn by the author. Lemma 8 is used in the proof of Lemma 6, but it is not correct. Lemma 6 is essential for the main results.