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pro vyhledávání: '"P. Balanescu"'
Let $I_{n,m} = (x_1\cdots x_{m},x_2 \cdots x_{m+1},\ldots,x_{n+1}x_{n+2}\cdots x_{n+m})$ be the $m$-path ideal of a path of length $n + m-1$ over a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_{n+m}]$. We compute all the graded Betti numbers of all p
Externí odkaz:
http://arxiv.org/abs/2405.04747
Let $J_{n,m} = (x_1\cdots x_{m},x_2 \cdots x_{m+1},\ldots,x_{n}x_1\cdots x_{m-1})$ be the $m$-path ideal of a cycle of length $n \ge 5$ over a polynomial ring $S = k[x_1,\ldots,x_n]$. Let $t\geq 1$ be an integer. We show that $J_{n,m}^t$ has a linear
Externí odkaz:
http://arxiv.org/abs/2404.17880
Autor:
Cimpoeas, Mircea, Balanescu, Silviu
Given a numerical function $h:\mathbb Z_{\geq 0}\to\mathbb Z_{\geq 0}$ with $h(0)>0$, the Hilbert depth of $h$ is $\operatorname{hdepth}(h)=\max\{d\;:\;\sum\limits_{j=0}^k (-1)^{k-j}\binom{d-j}{k-j}h(j)\geq 0\text{ for all }k\leq d\}$; see arXiv:2309
Externí odkaz:
http://arxiv.org/abs/2402.01478
Autor:
Balanescu, Silviu, Cimpoeas, Mircea
Let $J_{n,m}:=(x_1x_2\cdots x_m,\; x_2x_3\cdots x_{m+1},\; \ldots,\; x_{n-m+1}\cdots x_n,\; x_{n-m+2}\cdots x_nx_1, \ldots, x_nx_1\cdots x_{m-1})$ be the $m$-path ideal of the cycle graph of length $n$, in the ring of polynomials $S=K[x_1,\ldots,x_n]
Externí odkaz:
http://arxiv.org/abs/2401.15594
Autor:
Balanescu, Silviu, Cimpoeas, Mircea
Let $\mathbf m=(x_1,\ldots,x_n)$ be the maximal graded ideal of $S:=K[x_1,\ldots,x_n]$. We present a new method for computing the Hilbert depth of powers of $\mathbf m$.
Comment: 11 pages; we realized that the main result was known in literature
Comment: 11 pages; we realized that the main result was known in literature
Externí odkaz:
http://arxiv.org/abs/2311.11079
Autor:
Balanescu, Silviu, Cimpoeas, Mircea
Let $K$ be a infinite field, $S=K[x_1,\ldots,x_n]$ and $0\subset I\subsetneq J\subset S$ two squarefree monomial ideals. In a previous paper we proved a new formula for the Hilbert depth of $J/I$. In this paper, we illustrate how one can use the Stan
Externí odkaz:
http://arxiv.org/abs/2310.12339
Autor:
Balanescu, Silviu, Cimpoeas, Mircea
Let $h:\mathbb Z \to \mathbb Z_{\geq 0}$ be a nonzero function with $h(k)=0$ for $k\ll 0$. We define the Hilbert depth of $h$ by $\operatorname{hdepth}(h)=\max\{d\;:\; \sum_{j\leq k} (-1)^{k-j}\binom{d-j}{k-j}h(j)\geq 0\text{ for all }k\leq d\}$. We
Externí odkaz:
http://arxiv.org/abs/2309.10521
Publikováno v:
Romanian Journal of Rheumatology, Vol 27, Iss 2 (2018)
Sarcoidosis is an inflammatory disease of unknown etiology, characterized by non-caseating epithelioid granulomas. Neurological involvement appears in 5-10% of cases, most frequently leading to involvement of the cranial nerves, the hypothalamus and
Externí odkaz:
https://doaj.org/article/25c1c6f99ad4433db699b6da0fd73be3
Autor:
Balanescu, Silviu, Cimpoeas, Mircea
Let $K$ be a field, $A$ a standard graded $K$-algebra and $M$ a finitely generated graded $A$-module. Inspired by our previous works, we study the Hilbert depth of $h_M$, that is $$\operatorname{hdepth}(h_M)=\max\{d\;:\; \sum\limits_{j\leq k} (-1)^{k
Externí odkaz:
http://arxiv.org/abs/2308.14031
Autor:
Balanescu, Silviu, Cimpoeas, Mircea
Let $K$ be a field and $S=K[x_1,\ldots,x_n]$, the ring of polynomials in $n$ variables, over $K$. Using the fact that the Hilbert depth is an upper bound for the Stanley depth of a quotient of squarefree monomial ideals $0\subset I\subsetneq J\subset
Externí odkaz:
http://arxiv.org/abs/2307.03018