The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

For positive integers n and l, we study the cyclic u(gl n )-module generated by the l-th power of the α-determinant det (α) (X). This cyclic module is isomorphic to the n-th tensor space S¹(𝕔 n ) ⊕n ...

It is known that there exist many pairs of nonisomorphic graphs which have the same set of eigenvalues, even when counting multiplicities. Such graphs have identical characteristic polynomials (of ...