Related papers: Tissus alg\'ebriques exceptionnels

For a row-finite higher-rank graph {\Lambda}, we construct a higher-rank graph T{\Lambda} such that the Toeplitz algebra of {\Lambda} is isomorphic to the Cuntz-Krieger algebra of T{\Lambda}. We then prove that the higher-rank graph…

For each natural number $n$, we define a category whose objects are discriminant algebras in rank $n$, i.e. functorial means of attaching to each rank-$n$ algebra a quadratic algebra with the same discriminant. We show that the discriminant…

An $L$-matrix is a matrix whose off-diagonal entries belong to a set $L$, and whose diagonal is zero. Let $N(r,L)$ be the maximum size of a square $L$-matrix of rank at most $r$. Many applications of linear algebra in extremal combinatorics…

In this paper, we make progress on a question related to one of Galvin that has attracted substantial attention recently. The question is that of determining among all graphs $G$ with $n$ vertices and $\Delta(G)\leq r$, which has the most…

We consider the problem of classifying (possibly noncommutative) R-algebras of low rank over an arbitrary base ring R. We first classify algebras by their degree, and we relate the class of algebras of degree 2 to algebras with a standard…

A solution to a problem of Erd\H{o}s, Rubin and Taylor is obtained by showing that if a graph $G$ is $(a:b)$-choosable, and $c/d > a/b$, then $G$ is not necessarily $(c:d)$-choosable. The simplest case of another problem, stated by the same…

We are interested by holomorphic $d$-webs $W$ of codimension one in a complex $n$-dimensional manifold $M$. If they are ordinary, i.e. if they satisfy to some condition of genericity (whose precise definition is recalled), we proved in [CL]…

Alspach [ Bull. Inst. Combin. Appl., 52 (2008), pp. 7-20] defined the maximal matching sequencibility of a graph $G$, denoted $ms(G)$, to be the largest integer $s$ for which there is an ordering of the edges of $G$ such that every $s$…

Let $\bar{G} = (G, \omega)$ be a vertex-weighted graph, and $\delta$ a divisor class on $G$. Let $r_{\bar{G}}(\delta)$ denote the combinatorial rank of $\delta$. Caporaso has introduced the algebraic rank…

Let $K$ be a complete discrete valued field of characteristic $p$ with residue $k$ which is not necessarily perfect. We prove the Conjecture in \cite{cs} that a $p$-algebra over $K$ contains a totally ramified cyclic maximal subfield if it…

We show that for several notions of rank including tensor rank, Waring rank, and generalized rank with respect to a projective variety, the maximum value of rank is at most twice the generic rank. We show that over the real numbers, the…

We introduce the notion of basic superrank for varieties of algebras which generalizes that of basic rank. First we consider a number of varieties of nearly associative algebras over a field of characteristic $0$ that have infinite basic…

The main change with respect to the previous version is a change of terminology : we call "ordinary" the webs previously called "regular". A holomorphic $d$-web of codimension one in dimension $n$ is "ordinary", if it satisfies to some…

We classify Artin-Schreier extensions of valued fields with non-trivial defect according to whether they are connected with purely inseparable extensions with non-trivial defect, or not. We use this classification to show that in positive…

Grosu [On the algebraic and topological structure of the set of Tur\'{a}n densities. \emph{J. Combin. Theory Ser. B} \textbf{118} (2016) 137--185] asked if there exist an integer $r\ge 3$ and a finite family of $r$-graphs whose Tur\'{a}n…

We prove the following theorems: Theorem 1: For any E-field with cyclic kernel, in particular $\mathbb C$ or the Zilber fields, all real abelian algebraic numbers are pointwise definable. Theorem 2: For the Zilber fields, the only pointwise…

We introduce a new link invariant called the algebraic genus, which gives an upper bound for the topological slice genus of links. In fact, the algebraic genus is an upper bound for another version of the slice genus proposed here: the…

Let A be a unital maximal full algebra of operator fields with base space the k-cube [0,1]^k and fibre algebras, say, {A_t}_{t \in [0,1]^k}. Then the stable rank of A is bounded above by the supremum of the stable ranks sr(C([0,1]^k)…

We show that if G is a graph of sufficiently large order n containing as many r-cliques as the r-partite Turan graph of order n; then for some C>0 G has more than Cn^(r-1) (r+1)-cliques sharing a common edge unless G is isomorphic to the…

We give various results and applications using the connection $(E,\nabla)$ associated with a $d$-web. Precisely, we exhibit fundamental invariants of the web related to the differential equation of first order which presents the web. They…