1
Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore 54600, Pakistan
2
Faculty of Mathematics and Computer Science, Ovidius University Bd. Mamaia 124, 900527 Constanta, and Lumina-The University of South-East Europe Sos. Colentina nr. 64b, Bucharest, Romania
3
Faculty of Mathematics and Computer Science, Ovidius University, Bd.\ Mamaia 124, 900527 Constanta, Romania, and Simion Stoilow Institute of Mathematics of the Romanian Academy, Research group of the project ID-PCE-2011-1023, P.O.Box 1-764, Bucharest 014700, Romania
Abstract
Let $X=\left(
\begin{array}{llll}
x_1 & \ldots & x_{n-1}& x_n\\
x_2& \ldots & x_n & x_{n+1}
\end{array}\right)$ be the Hankel matrix of size $2\times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_G\subset K[x_1,\ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaulay. We find the minimal primes of $I_G$ and show that $I_G$ is a set theoretical complete intersection. Moreover, a sharp upper bound for the regularity of $I_G$ is given.
Chaudhry, F., Dokuyucu, A., & Ene, V. (2015). Binomial edge ideals and rational normal scrolls. Bulletin of the Iranian Mathematical Society, 41(4), 971-979.
MLA
Chaudhry, F., Dokuyucu, A., & Ene, V. "Binomial edge ideals and rational normal scrolls", Bulletin of the Iranian Mathematical Society, 41, 4, 2015, 971-979.
HARVARD
Chaudhry F., Dokuyucu A., Ene V. (2015). 'Binomial edge ideals and rational normal scrolls', Bulletin of the Iranian Mathematical Society, 41(4), pp. 971-979.
CHICAGO
F. Chaudhry, A. Dokuyucu & V. Ene, "Binomial edge ideals and rational normal scrolls," Bulletin of the Iranian Mathematical Society, 41 4 (2015): 971-979,
VANCOUVER
Chaudhry F., Dokuyucu A., Ene V. Binomial edge ideals and rational normal scrolls. BIMS. 2015;41(4):971-979.
