Regular Sequences of Symmetric Polynomials
... evaluated at q jFj gives exactly the number of F-subspaces of F nd of dimension n, [S, 1.3.18]. It is also known that the coefficient of qk in Pd;n (q) is the number of partitions of k with at most n parts and parts bounded by d, [S, 1.3.19]. This interpretation leads to the following constructio ...
... evaluated at q jFj gives exactly the number of F-subspaces of F nd of dimension n, [S, 1.3.18]. It is also known that the coefficient of qk in Pd;n (q) is the number of partitions of k with at most n parts and parts bounded by d, [S, 1.3.19]. This interpretation leads to the following constructio ...
MTH299 Final Exam Review 1. Describe the elements
... 16. Prove or disprove the statement: there exists an integer n such that n2 − 3 = 2n. 17. Prove or disprove the statement: there exists a real number x such that x4 + 2 = 2x2 . 18. Prove that there exists a unique real number x such that x3 + 2 = 2x. ...
... 16. Prove or disprove the statement: there exists an integer n such that n2 − 3 = 2n. 17. Prove or disprove the statement: there exists a real number x such that x4 + 2 = 2x2 . 18. Prove that there exists a unique real number x such that x3 + 2 = 2x. ...
