Open Problems in Computable Algebra and Combinatorics

			  Jeffrey B. Remmel
		      Department of Mathematics
		  University of California, San Diego

One can look at the effective content of theorems in algebra and
combinatorics from a number of different points of view depending on the
underlying computation model. For example, computable algebra and
combinatorics assumes that the underlying models have computable
universes, relations, and functions.  Polynomial time algebra and
combinatorics assumes that the underlying models have polynomial time
universes, relations, and functions.  Automatic algebra and combinatorics
assumes that the underlying universes, relations, and functions, viewed as
relations, can be recognized by automata.  We will compare and contrast
these various points of view and give selected survey of open problems and
new avenues of research in effective algebra and combinatorics for a
variety of computation models.