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We show that the "double circle" order type and some of its generalizations have a compatible triangulation with any other order types with the same number of points and number of edges on convex hull, thus proving another special case of…

The article presents the proof of Casas-Alvero conjecture.

Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.

In this paper we prove the probabilistic continuous complexity conjecture. In continuous complexity theory, this states that the complexity of solving a continuous problem with probability approaching 1 converges (in this limit) to the…

In this paper, we extend the rectangular side of the shuffle conjecture by stating a rectangular analogue of the square paths conjecture. In addition, we describe a set of combinatorial objects and one statistic that are a first step…

We propose an efficient algorithm for computing a common eigenvector of a finite set of square matrices. As an immediate consequence we obtain an algorithm for determining whether the matrices admit a simultaneous triangulation, and, if so,…

Let $\mathcal{A}=(A_{1},...,A_{n},...)$ be a finite or infinite sequence of $2\times2$ matrices with entries in an integral domain. We show that, except for a very special case, $\mathcal{A}$ is (simultaneously) triangularizable if and only…

The Jacobian Conjecture would follow if it were known that real polynomial maps with a unipotent Jacobian matrix are injective. The conjecture that this is true even for $C^1$ maps is explored here. Some results known in the polynomial case…

In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.

In this paper, we proved a special case of the DDVV Conjecture.

A conjecture concerning some pairs of interfering estimates for some integrals is formulated in three equivalent versions. Its importance for the the Paley problem for plurisubharmonic functions and for certain classes of extremal problems…

We prove Simon's conjecture for 3-manifolds.

We present a conjecture about partitions, with a very elementary formulation.

For a matrix $A$ which satisfies Crouzeix's conjecture, we construct several classes of matrices from $A$ for which the conjecture will also hold. We discover a new link between cyclicity and Crouzeix's conjecture, which shows that…

We present counterexamples to a 30-year-old conjecture of Las Vergnas [J. Combin. Theory Ser. B, 1988] regarding the Tutte polynomial of binary matroids.

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

In this paper we obtain a partial answer to a conjecture on the solvabilty of linear difference equations in quasianalytic Carleman classes.

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

We revisit a formula that connects the minimal ranks of triangular parts of a matrix and its inverse and relate the result to structured rank matrices. We also address the generic minimal rank problem.

Gronwall conjecture states that a planar 3-web which admits more than one distinct linearization is locally equivalent to an algebraic web. We give a partial answer to the conjecture in the affirmative for the class of planar 3-webs with…