The number of outside corners of monomial ideals Original Research Article

The outside corners of a monomial ideal are the maximal standard monomials modulo that ideal. Let cn(p) be the maximal number of outside corners of any monomial ideal generated by p monomials in n variables. We show that cn(p) = minus sign in circle(p[n/2]) for fixed n. An exact calculation for n = 4 shows that the function cn(p) is not a polynomial in p.