The Weak Lefschetz Property of Whiskered Graphs
摘要
We consider Artinian level algebras arising from the whiskering of a graph. Employing a result by Dao-Nair we show that multiplication by a general linear form has maximal rank in degrees 1 and $$n-1$$ when the characteristic is not two, where n is the number of vertices in the graph. Moreover, the multiplication is injective in degrees $$