Defining functions on equivalence classes

Some equivalence classes of operators on B(H)

Uniformly Defining Complexity Classes of Functions

We introduce a general framework for the definition of function classes. Our model, which is based on polynomial time nondeterministic Turing transducers, allows uniform characterizations of FP, FPNP, counting classes (# P, # NP, # coNP, GapP, GapPNP), optimization classes (max P, min P, max NP, min NP), promise classes (NPSV, #few P, c# P), multivalued classes (FewFP, NPMV) and many more. Each...

Equivalence classes of functions between finite groups

Two types of equivalence relation are used to classify functions between finite groups into classes which preserve combinatorial and algebraic properties important for a wide range of applications. However, it is very difficult to tell when functions equivalent under the coarser (“graph”) equivalence are inequivalent under the finer (“bundle”) equivalence. Here we relate graphs to transversals ...

The number of classes of choice functions under permutation equivalence

A choice function f of an n-set X is a function whose domain is the power set P(X), and whose range is X, such that f(A) E A for each A ~ X. If k is a fixed positive integer, k :::; n, by a k-restricted choice function we mean the restriction of some choice function to the collection of k-subsets of X. The symmetric group Sx acts, by natural extension on the respective collections C(X) of choic...

Zeta Functions for Equivalence Classes of Binary Quadratic Forms

They are sums of zeta functions for prehomogeneous vector spaces and generalizations of Epstein zeta functions. For the rational numbers and imaginary quadratic fields one can define these functions also for SL(2, ^-equivalence, which for convenience we call 1equivalence. The second function arises in the calculation of the Selberg trace formula for integral operators on L(PSL(2, (!?)\H) where ...