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This paper has been withdrawn by the author due to a crucial sign error in Theorem 3.4.

In this note we show that the well known coincidence results for scalar-valued homogeneous polynomials can not be generalized in some natural directions.

This paper has been withdrawn by the author(s), due to a crucial error in eq. 6.

This paper has been withdrawn by the author due to a crucial error in the submission action.

A formula of Stembridge states that the permutation peak polynomials and descent polynomials are connected via a quadratique transformation. The aim of this paper is to establish the cycle analogue of Stembridge's formula by using cycle…

This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set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

Paper withdrawn. Error lemma 7.

This paper has been withdrawn by the author due to a crucial mistakes.

This paper is withdrawn.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

This paper has been withdrawn by the authors due to a more research needed to estimate $h^{*}_{n}(b)$ which really should be written as $h^{*}_{n}(b,A)$ for $b\in \Gamma (t)$.

This paper has been withdrawn by the author due a few mistakes in the paper.

Sorry, there are some calculation errors in this paper

This paper has been withdrawn by the authors due to a crucial error.

This paper has been withdrawn by the author due to crucial sign error in Lemma 8.1.

This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.

This paper has been withdrawn by the author due to an error.

This paper has been withdrawn by the author(s), due a crucial i-number error in Eqn. 18.

The methods used to prove the main result must be incorrect, as they can be used to arrive at a contradiction with previously known results. Thus the paper was withdrawn.