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- 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)

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)

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 formal mathematical theory of fair division has a rich history dating back at least to Steinhaus in the 1940's [Ste1, Ste2, Ste3, Ste4]. In recent work in this area, several general classes of errors have appeared along with confusion about the necessity and sufficiency of certain hypotheses. It is the purpose of this article to correct the scientific… (More)

The combinatorial theory of species developed by Joyal provides a foundation for enumerative combinatorics of objects constructed from finite sets. In this paper we develop an analogous theory for the enumerative combinatorics of objects constructed from vector spaces over finite fields. Examples of these objects include subspaces, flags of subspaces,… (More)

The semigroup game is a two-person zero-sum game defined on a semigroup (S, ·) as follows: Players 1 and 2 choose elements x ∈ S and y ∈ S, respectively, and player 1 receives a payoff f (xy) defined by a function f : S → [−1, 1]. If the semigroup is amenable in the sense of Day and von Neumann, one can extend the set of classical strategies, namely… (More)

- Theodore P Hill, Kent E Morrison, Stanford, G ¨ Ottingen, Berkeley, M A
- 2010

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 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)

In a guessing game, players guess the value of a random real number selected using some probability density function. The winner may be determined in various ways; for example, a winner can be a player whose guess is closest in magnitude to the target, or a winner can be a player coming closest without guessing higher than the target. We study optimal… (More)

In scientific computations using floating point arithmetic, rescaling a data set multiplicatively (e.g., corresponding to a conversion from dollars to euros) changes the distribution of the mantissas, or fraction parts, of the data. A scale-distortion factor for probability distributions is defined, based on the Kantorovich distance between distributions.… (More)