The polynomial degrees of Grassmann and Segre varieties over GF(2)

A recent proof that the Grassmannian G1;n;2 of lines of PG(n; 2) has polynomial degree n 2 1 is outlined, and is shown to yield a theorem about certain kinds of subgraphs of any (simple) graph = (V; E) such that jEj < jVj: Somewhat similarly, the polynomial degree of the Segre variety Sm;n;2; m n; is shown to be mn + m; and in consequence a graph theory result is obtained about certain subgraphs of any graph which is a subgraph of the complete bipartite graph Km+1;n+1:

• Type: Journal
• Year: 2008
• Where: DM
• Authors: R. Shaw
• Keywords: Certain Kinds, DM 2008, Polynomial, Polynomial Degree