Related papers: Comment on revised version of "The Hadamard circul…

It is shown that a recent article by Z.-D. Zhang [arXiv:0705.1045] is in error and violates well-known theorems.

The Shuffle Theorem of Carlsson and Mellit gives a combinatorial expression for the bigraded Frobenius characteristic of the ring of diagonal harmonics, and the Delta Conjecture of Haglund, Remmel and the second author provides two…

The paper was withdrawn because of its significant overlap with a paper appeared recently.

This paper has been withdrawn by the authors, due an error in Theorem 3.1 : the induced module is not in general a submodule.

We review the derivations and conclusions made in Caravelli and Modesto (2010 \textit{Class. Quantum Grav.} \textbf{27} 245022, arXiv:1006.0232) and show that most of the analysis performed there is not valid.

We prove the Schr\"oder case, i.e. the case $\langle \cdot,e_{n-d}h_d \rangle$, of the conjecture of Haglund, Remmel and Wilson (Haglund et al. 2018) for $\Delta_{h_m}\Delta_{e_{n-k-1}}'e_n$ in terms of decorated partially labelled Dyck…

This article demonstrates that the recent proof of the invariant subspace problem, as presented by Khalil et al., is incorrect.

This paper is incorrect, and has been withdrawn by the author.

Recently, Hong Wang and Joshua Zahl announced a proof of the 3-dimensional Kakeya conjecture. This is a survey article on the proof of Kakeya. We introduce the problem, discuss previous work and some of the difficulties of the problem, and…

The paper has been withdrawn due to numerical error.

We prove a metrical result on a family of conjectures related to the Littlewood conjecture, namely the original Littlewood conjecture, the mixed Littlewood conjecture of de Mathan and Teuli\'e and a hybrid between a conjecture of Cassels…

We survey recent developments on the Restriction conjecture.

In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].

Withdrawn -- a revised version will appear in due course.

This is erratum of the paper [Phys. Rev. Lett. {\bf 84}, 4260 (2000)]

In this paper we disprove the Haagerup statement that all complex Hadamard matrices of order five are equivalent with the Fourier matrix $F_5$ by constructing circulant matrices that lead to new Hadamard matrices. An important item is the…

This paper has been withdrawn by the authors. We have discovered an error in the evaluation of the diagram, which invalidates our conclusion.

We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for $|q_0|=...=|q_{N-1}|=1$ the quantity…

We prove some combinatorial results related to a formula on Hodge integrals conjectured by Mari\~no and Vafa. These results play important roles in the proof and applications of this formula by the author jointly with Chiu-Chu Melissa Liu…

It is shown that ''Theorem 1'' of the article ''Copenhagen Interpretation of Quantum Mechanics Is Incorrect'' by G.-L. Li and V.O.K. Li (see quant-ph/0509089) is false. Therefore the assertion expressed in the title of that article is…