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pro vyhledávání: '"Tohaneanu, Stefan"'
Yuzvinsky and Rose-Terao have shown that the homological dimension of the gradient ideal of the defining polynomial of a generic hyperplane arrangement is maximum possible. In this work one provides yet another proof of this result, which in addition
Externí odkaz:
http://arxiv.org/abs/2408.13579
It is well-known that the first generalized Hamming weight of a code, more commonly called \textit{the minimum distance} of the code, corresponds to the initial degree of the Stanley-Reisner ideal of the matroid of the dual code. Our starting point i
Externí odkaz:
http://arxiv.org/abs/2406.13658
Autor:
Tohaneanu, Stefan O.
In this note we show that the minimum distance of a linear code equals one plus the smallest shift in the first step of the minimal graded free resolution of the Orlik-Terao algebra (i.e., the initial degree of the Orlik-Tearo ideal) constructed from
Externí odkaz:
http://arxiv.org/abs/2311.03688
Autor:
Pawlina, John, Tohaneanu, Stefan
Let \({\mathbb K}\) be any field, let \(X\subset {\mathbb P}^{k-1}\) be a set of \(n\) distinct \({\mathbb K}\)-rational points, and let \(a\geq 1\) be an integer. In this paper we find lower bounds for the minimum distance \(d(X)_a\) of the evaluati
Externí odkaz:
http://arxiv.org/abs/2310.00102
Autor:
Tohaneanu, Stefan Ovidiu
This dissertation uses methods from homological algebra and computational commutative algebra to study four problems. We use Hilbert function computations and classical homology theory and combinatorics to answer questions with a more applied mathema
Externí odkaz:
http://hdl.handle.net/1969.1/5789
Let $\mathcal{A}$ denote a central hyperplane arrangement of rank $n$ in affine space $\mathbb{K}^n$ over an infinite field $\mathbb{K}$ and let $l_1,\ldots, l_m\in R:= \mathbb K[x_1,\ldots,x_n]$ denote the linear forms defining the corresponding hyp
Externí odkaz:
http://arxiv.org/abs/2101.02735
Autor:
Burity, Ricardo, Tohaneanu, Stefan
In this paper we give full classification of rank 3 line arrangements in $\mathbb P^2$ (over a field of characteristic 0) that have a minimal logarithmic derivation of degree 3. The classification presents their defining polynomials, up to a change o
Externí odkaz:
http://arxiv.org/abs/2005.14367
Given $\Sigma\subset R:=\mathbb K[x_1,\ldots,x_k]$, where $\mathbb K$ is a field of characteristic 0, any finite collection of linear forms, some possibly proportional, and any $1\leq a\leq |\Sigma|$, we prove that $I_a(\Sigma)$, the ideal generated
Externí odkaz:
http://arxiv.org/abs/2004.07430
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Autor:
Tohaneanu, Stefan, Xie, Yu
Let $\Sigma$ be a finite collection of linear forms in $\mathbb K[x_0,\ldots,x_n]$, where $\mathbb K$ is a field. Denote ${\rm Supp}(\Sigma)$ to be the set of all nonproportional elements of $\Sigma$, and suppose ${\rm Supp}(\Sigma)$ is generic, mean
Externí odkaz:
http://arxiv.org/abs/1906.08346