Discrete math/Combinatorics
a. Can you describe the number of fixed points of permutation "w" in terms of P(w)? (Hint : number of columns that satisfy a certain condition)
b. can you prove 1 * 3 * 5 * ... * (2n-1) = sum (# of SYT (Standard Young Tableaus) of shape lambda), where you sum over all partition lambdas of 2n, such that its conjugate only has even parts?