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On matrix and lattice ideals of digraphs | ||
| Transactions on Combinatorics | ||
| مقاله 4، دوره 7، شماره 2، شهریور 2018، صفحه 35-46 اصل مقاله (246.57 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2017.105701.1510 | ||
| نویسندگان | ||
| Hamid Damadi1؛ Farhad Rahmati* 2 | ||
| 1Department of Mathematics, Amirkabir University of Technology (Tehran Polytechnic) Tehran, Iran. | ||
| 2Amirkabir University of Technology | ||
| چکیده | ||
| Let $\textit{G}$ be a simple, oriented connected graph with $n$ vertices and $m$ edges. Let $I(\textbf{B})$ be the binomial ideal associated to the incidence matrix \textbf{B} of the graph $G$. Assume that $I_L$ is the lattice ideal associated to the rows of the matrix $\textbf{B}$. Also let $\textbf{B}_i$ be a submatrix of $\textbf{B}$ after removing the $i$-th row. We introduce a graph theoretical criterion for $G$ which is a sufficient and necessary condition for $I(\textbf{B})=I(\textbf{B}_i)$ and $I(\textbf{B}_i)=I_L$. After that we introduce another graph theoretical criterion for $G$ which is a sufficient and necessary condition for $I(\textbf{B})=I_L$. It is shown that the heights of $I(\textbf{B})$ and $I(\textbf{B}_i)$ are equal to $n-1$ and the dimensions of $I(\textbf{B})$ and $I(\textbf{B}_i)$ are equal to $m-n+1$; then $I(\textbf{B}_i)$ is a complete intersection ideal. | ||
| کلیدواژه‌ها | ||
| Directed graph؛ Binomial ideal؛ Matrix ideals | ||
| مراجع | ||
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