Related papers: The solution of the complete nontrivial cycle inte…

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical…

The cyclic n-roots problem is an important benchmark problem for polynomial system solvers. We consider the pruning of cone intersections for a polyhedral method to compute series for the solution curves.

We provide a permutation-invariant version of the Koml\'os' theorem for non-negative random variables. The proof is quite elementary in the sense that it did not use the Axiom of Choice, and was based on a recent result in [3].

Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.

We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation problem. In the former case we obtain the same main result…

A transitive permutation group of prime degree is doubly transitive or solvable. We give a direct proof of this theorem by Burnside which uses neither S-ring type arguments, nor representation theory.

We give several algorithms addressing computations of intersections of conjugate subgroups.

Unimodal (i.e. single-humped) permutations may be decomposed into a product of disjoint cycles. Some enumerative results concerning their cyclic structure -- e.g. 2/3 of them contain fixed points -- are given. We also obtain in effect a…

We prove Union-Closed sets conjecture.

We prove that the quiver problem is NP complete.

Let $k$ be the function field of a complex curve or the field $C((t))$. We show that for a smooth complete intersection $X$ of $r$ hypersurfaces in $P^n_k$ of respective degrees $d_1,...,d_r$ with $\sum d_i^2\leq n+1$ the R-equivalence on…

We give a new expression for the number of factorizations of a full cycle into an ordered product of permutations of specified cycle types. This is done through purely algebraic means, extending work of Biane. We deduce from our result a…

In the present work, firstly, we use a minimax equality to prove the existence of a solution of certain system of varitional equations and we provide a numerical approximation of such a solution. Then, we propose a numerical method to solve…

We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a…

This paper proves a deformation circle pattern theorem, which gives a complete description of those circle patterns with interstices in terms of the combinatorial type, the exterior intersections angles and the conformal structures of…

We give a Belyi-type characterisation of smooth complete intersections of general type over $\mathbb{C}$ which can be defined over $\bar{\mathbb{Q}}$. Our proof uses the higher-dimensional analogue of the Shafarevich boundedness conjecture…

For the Odd Cycle Transversal problem, the task is to find a small set $S$ of vertices in a graph that intersects every cycle of odd length. The Subset Odd Cycle Transversal problem requires S to intersect only those odd cycles that include…

We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with…

An infinite permutation is a linear ordering of the set of non-negative integers. Generally, the properties of infinite permutations analogous to those of infinite words show some resemblances and some differences between permutations and…