A Large, Finite Permutation of Specific, Discrete Variants: Dan Graham’s Children’s Pavilion at Chambres d’Amis (1986)

Specific permutation polynomials over finite fields

We present new classes of permutation polynomials over finite fields. If q is the order of a finite field, some polynomials are of form xrf(x(q−1)/d), where d|(q − 1). Other permutation polynomials are related with the trace function. 2000 Mathematics Subject Classification: Primary 11T06.

A Worldly Look at Language Acquisition Dan

Finite Permutation Groups

1 Multiply transitive groups Theorem 1.1. Let Ω be a finite set and G ≤ Sym(Ω) be 2–transitive. Let N E G be a minimal normal subgroup. Then one of the following holds: (a) N is regular and elementary abelian. (b) N is primitive, simple and not abelian. Proof. First we show that N is unique. Suppose that M is another minimal normal subgroup of G, so N ∩M = {e} and therefore [N,M ] = {e}. Since ...

Finite Permutation Groups and Finite Simple Groups

In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced. Of course, the solution will have a considerable effect on many related areas, both wi...

Optimal Finite-time Control of Positive Linear Discrete-time Systems

This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...