论文标题
某些图的符号力量的规律性
Regularity of symbolic powers of certain graphs
论文作者
论文摘要
令$ g_ {n，r} $用$ n $ vertices $ \ {x_1，\ ldots，x_n \} $按循环顺序进行，对于每个顶点$ x_i $，请考虑集合$ a_i = \ {x_ {x_ {i-r}，\ ldots，x_ {i-1}，x_ {i+1}，x_ {i+2}，\ ldots，x_ {i+r} \}，$ $ 0 \ leq r \ leq \ bigl \ lfloor \ dfrac {n} {2} {2} \ bigr \ rfloor -1 $。在$ g_ {n，r} $中，每个顶点$ x_i $都与$ v（g_ {n，r}）\ backslash a_i $的所有顶点相邻。令$ i = i（g_ {n，r}）$为$ g_ {n，r} $的边缘理想。我们表明，明尼的猜想是$ i，$ $，即普通权力的规律性和$ i $的符号权力是相同的。我们计算整个班级的Waldschmidt常数和复兴。
Let $G_{n,r}$ denote the graph with $n$ vertices $\{x_1,\ldots,x_n\}$ in cyclic order and for each vertex $x_i$ consider the set $A_i=\{x_{i-r},\ldots,x_{i-1},x_{i+1},x_{i+2},\ldots, x_{i+r}\},$ where $x_{i-j}$ is the vertex $x_{n+i-j}$, whenever $i<j$ and $0\leq r\leq \Bigl\lfloor\dfrac{n}{2}\Bigr\rfloor -1$. In $G_{n,r}$, every vertex $x_i$ is adjacent to all the vertices of $V(G_{n,r})\backslash A_i$. Let $I=I(G_{n,r})$ be the edge ideal of $G_{n,r}$. We show that Minh's conjecture is true for $I,$ i.e. regularity of ordinary powers and symbolic powers of $I$ are equal. We compute the Waldschmidt constant and resurgence for the whole class.
