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pro vyhledávání: '"De Paris, Alessandro"'
Autor:
De Paris, Alessandro
To investigate hyperbinary expansions of a nonnegative integer $n$, an edge-labelled directed graph $A(n)$ has recently been introduced. After pointing out some new simple facts about its cyclomatic number, we give a relatively simple description of
Externí odkaz:
http://arxiv.org/abs/2410.01422
Autor:
De Paris, Alessandro
Motivated by the search for a deeper understanding of tensor rank, in view of its computational complexity applications, we investigate a possible path to determine the maximum symmetric rank in given degree and dimension. We work in terms of Waring
Externí odkaz:
http://arxiv.org/abs/2309.01414
We explicitly fix a mistake in a preliminary statement of our previous paper on the conductor at a multiplanar singularity. The correction is not immediate and, though the mistake does not affect correctness of the subsequent results, the wrong state
Externí odkaz:
http://arxiv.org/abs/1903.01121
Autor:
De Paris, Alessandro
We exhibit, for each even degree, a ternary form of rank strictly greater than the maximum rank of monomials. Together with an earlier result in the odd case, this gives the lower bound \[\operatorname{r_{max}}(3,d)\ge\left\lfloor\frac{d^2+2d+5}4\rig
Externí odkaz:
http://arxiv.org/abs/1706.04604
We discuss a possible noncommutative generalization of the notion of an equivariant vector bundle. Let $A$ be a $\mathbb{K}$-algebra, $M$ a left $A$-module, $H$ a Hopf $\mathbb{K}$-algebra, $\delta:A\to H\otimes A:=H\otimes_{\mathbb{K}} A$ an algebra
Externí odkaz:
http://arxiv.org/abs/1606.09130
Autor:
De Paris, Alessandro
Publikováno v:
Final version in Linear Algebra Appl. 500 (2016) 15--29
Let $\operatorname{r_{max}}(n,d)$ be the maximum Waring rank for the set of all homogeneous polynomials of degree $d>0$ in $n$ indeterminates with coefficients in an algebraically closed field of characteristic zero. To our knowledge, when $n,d\ge 3$
Externí odkaz:
http://arxiv.org/abs/1510.08048
Autor:
De Paris, Alessandro
Publikováno v:
Int. J. Algebra Comput. 25, No. 4, 607-631 (2015)
To our knowledge at the time of writing, the maximum Waring rank for the set of all ternary forms of degree $d$ (with coefficients in an algebraically closed field of characteristic zero) is known only for $d\le 4$. The best upper bound that is known
Externí odkaz:
http://arxiv.org/abs/1409.7643
Autor:
Ballico, Edoardo, De Paris, Alessandro
Publikováno v:
Discrete Comput. Geom. (2017), 57(4), 896--914
A notion of open rank, related with generic power sum decompositions of forms, has recently been introduced in the literature. The main result here is that the maximum open rank for plane quartics is eight. In particular, this gives the first example
Externí odkaz:
http://arxiv.org/abs/1312.3494
Autor:
De Paris, Alessandro
Publikováno v:
Final version in Matematiche, 70, no. 2, 3-18 (2015)
At the time of writing, the general problem of finding the maximal Waring rank for homogeneous polynomials of fixed degree and number of variables (or, equivalently, the maximal symmetric rank for symmetric tensors of fixed order and in fixed dimensi
Externí odkaz:
http://arxiv.org/abs/1309.6475