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تسجيل مستخدم جديدOn the extremal Betti numbers of squarefree monomial ideals
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Let $K$ be a field and $S = K[x_1,dots,x_n]$ be a polynomial ring over $K$. We discuss the behaviour of the extremal Betti numbers of the class of squarefree strongly stable ideals. More precisely, we give a numerical characterization of the possible extremal Betti numbers (values as well as positions) of such a class of squarefree monomial ideals.
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Let $K$ be a field and let $S=K[x_1,dots,x_n]$ be a standard polynomial ring over a field $K$. We characterize the extremal Betti numbers, values as well positions, of a $t$-spread strongly stable ideal of $S$. Our approach is constructive. Indeed, g
iven some positive integers $a_1,dots,a_r$ and some pairs of positive integers $(k_1,ell_1),dots,(k_r,ell_r)$, we are able to determine under which conditions there exist a $t$-spread strongly stable ideal $I$ of $S$ with $beta_{k_i, k_iell_i}(I)=a_i$, $i=1, ldots, r$, as extremal Betti numbers, and then to construct it.
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