How are monomials used in the theory of invariants of algebraic groups?

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 ... It is important to understand when G is a Cohen-Macaulay ring, that is dim G = depthG; in this case, this is equivalent to (tg1 )∗ being a non-zerodivisor. For a matroid M and rank r, we associate a monomial ideal (a monomial variant of the Orlik–Solomon ideal) to the set of flats of M of rank at most r. In ... Mar 12, 2025 ... When dividing monomials, we need to remember our exponent rules, specifically the rule xmxn=xm−n . This means that when bases raised to ... Feb 4, 2025 ... Monomial Binomial and Trinomial. A monomial expression has, only one term. For example, 3xy is a monomial. A binary expression is one which has ... In this lesson, you will learn how to factor monomials. You will use what you already know about factoring integers to help you in this quest. Jun 3, 2016 ... monomials with higher than generic rank. Theorem 1. Let M be a monomial in n ≥ 4 variables and let d = deg M > 1. Then r(M) < rgen(n, d) ... Polynomials. polynomial—A monomial, or two or more monomials, combined by addition or subtraction monomial—A polynomial with exactly one term binomial— ... Apr 13, 2015 ... Are there standard formulas for the integral over a simplex of a monomial in the barycentric coordinates? Can someone supply a reference? Jun 25, 2021 ... Gathering monomial coefficients of orthogonal polynomials using SpecialPolynomials.jl ... While using SpecialPolynomials.jl I want to gather the ...