Algebra/Chapter 10/Symmetric Polynomials

Introduction In Algebra, a polynomial in several variables is called a symmetric polynomial if it remains invariant under any permutation of its variables. Symmetric polynomials were initially studied in the context of solutions of polynomial equations in a single variable, since the coefficients of the polynomial are symmetric polynomials in its roots. Over time, symmetric polynomials gained a status of their own, and they appear in various branches of mathematics, mainly in combinatorics. Chapters /Monomial Ordering/ /Permutations and Symmetry/ /Elementary Symmetric Polynomials/ /Fundamental Theorem of Symmetric Polynomials/