On the dimension of vertex labeling of $k$-uniform dcsl of an even cycle

Abstract

In this paper, we discuss the lower bound for the dcsl index $ \delta_k $ of a $k$-uniform dcsl of even cycle $ C_{2n},\ n\geq 2 $, in terms of the dimension of a poset and prove that $dim({\mathscr{F}})\leq \delta_k(C_{2n}) $, where ${\mathscr{F}}$ is the range of any $k$-uniform dcsl $ f $ of $ C_{2n},\ n\geq 2 $.