What are some interesting or surprising properties of monomials?

May 1, 2020 ... 1 Expert Answer ... Monomial, binomial, and trinomial are types of polynomials. A polynomial is an algebraic equation that consists of many (poly) ... Mar 7, 2005 ... sequence of monomials. Macaulay [Ma] showed in 1927 that all Hilbert functions over B = k[x1, ··· , xn] are attained by lex ideals. Definition: Monomial. A monomial is a single-term algebraic expression that is the product of constants and variables, where the variables only have nonnegative ... Jul 14, 2015 ... It is worth to try to understand at first monomial maps f(x) = x k. , since. - a best solution for q odd is a monomial map; and. - they are ... Sep 20, 2024 ... The main contribution of this paper is the introduction of a novel invariant of a monomial ideal, termed its signature. A monomial is one variable that is the product of a constant (a letter that stands just for one number) and a variable with a nonnegative integer power. monomial ideals. Proposition 56.1. (Gasharov-Hibi-Peeva, Miller) Let u ∈ M be a monomial, and consider the monomial ideal (M≤u) generated by the monomials ... May 9, 2021 ... Comments Section ... It's equal to a monomial when x ≠ 0, but why even address the question in the first place? Make sure the students know that a ... Aug 12, 2024 ... There's no such thing as a bare 'monomial' or 'polynomial'; that refers to the relationship between two variables. Lemma 1.2 Every monomial ideal has a unique minimal set of monomial generators, and this set is finite. Proof. The Hilbert Basis Theorem says that every ideal ...