Proof
... • “If n is odd and m ≡ 3 (mod 4), then (n2 + m) is divisible by 4.” (More complicated than midterm.) ...
... • “If n is odd and m ≡ 3 (mod 4), then (n2 + m) is divisible by 4.” (More complicated than midterm.) ...
the Catalan numbers
... µn is called the empirical eigenvalue distribution of the matrix W (n) . Notice that it is a random distribu(n) (n) tion, because for each n, the eigenvalues λ1 , . . . , λn are random. For a given realization of the λ(n) ’s, µn may still be interpreted as the distribution of one of these eigenvalue ...
... µn is called the empirical eigenvalue distribution of the matrix W (n) . Notice that it is a random distribu(n) (n) tion, because for each n, the eigenvalues λ1 , . . . , λn are random. For a given realization of the λ(n) ’s, µn may still be interpreted as the distribution of one of these eigenvalue ...
