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- Kent E. Morrison
- 1995

- Andrew J. Hetzel, Jay S. Liew, Kent E. Morrison
- The American Mathematical Monthly
- 2007

1. INTRODUCTION. It is natural to use integer matrices for examples and exercises when teaching a linear algebra course, or, for that matter, when writing a textbook in the subject. After all, integer matrices offer a great deal of algebraic simplicity for particular problems. This, in turn, lets students focus on the concepts. Of course, to insist on… (More)

The conjecture of Fisher and Hartwig, published in 1968, describes the asymptotic expansion of Toeplitz determinants with singular generating functions. For more than twenty years progress was made in extending the validity of the conjecture, but recent computer experiments led to counterexamples that show the limits of the original conjecture and pointed… (More)

- Kent E. Morrison
- 2006

In this expository article we collect the integer sequences that count several different types of matrices over finite fields and provide references to the Online Encyclopedia of Integer Sequences (OEIS). Section 1 contains the sequences, their generating functions, and examples. Section 2 contains the proofs of the formulas for the coefficients and the… (More)

- Kent E. Morrison
- 1995

A linear operator on a Hilbert space may be approximated with finite matrices by choosing an orthonormal basis of the Hilbert space. For an operator that is not compact such approximations cannot converge in the norm topology on the space of operators. Multiplication operators on spaces of L 2 functions are never compact; for them we consider how well the… (More)

- Kent E. Morrison
- ArXiv
- 2012

The game You walk into a casino, and just inside the main entrance you see a new game to play—the Multiplication Game. You sit at a table opposite the dealer and place your bet. The dealer hits a button and from a slot in the table comes a slip of paper with a number on it that you cannot see. You use a keypad to choose a number of your own—any positive… (More)

- Kent Morrison
- 2005

We determine the limiting distribution of the number of eigenvalues of a random n×n matrix over F q as n → ∞. We show that the q → ∞ limit of this distribution is Poisson with mean 1. The main tool is a theorem proved here on asymptotic independence for events defined by conjugacy class data arising from distinct irreducible polynomials. The proof of this… (More)

and his primary research interests are in mathematical probability, especially optimal-stopping theory, fair-division problems, and Benford's Law. where he received his Ph.D. and B.A. degrees. Currently he is a visiting researcher at the American Institute of Mathematics in Palo Alto. He has a number of research interests in the areas of algebra, geometry,… (More)

- KENT MORRISON
- 2004

For a finitely generated /^-algebra A and a finite dimensional ^-vector space M the representations of A on M form an affine ^-scheme Mod^(M). Of particular interest for this scheme are the connected components, the irreducible components, and the open and closed orbits under the natural action of the general linear group Aut A (M), since the orbits are the… (More)

The asymptotic expansions of Toeplitz determinants of certain symbols with multiple jump discontinuities are shown to satisfy a revised version of the conjecture of Fisher and Hartwig. The Toeplitz matrix T n [φ] is said to be generated by the function φ if T n [φ] = (φ i−j), i, j = 0,. .. , n − 1. where φ n = 1 2π 2π 0 φ(θ)e −inθ dθ is the nth Fourier… (More)