Decompositions of functions based on arity gap

Details Decompositions of functions based on arity gap Decompositions of functions based on arity gap

2010-03-05

arxiv.org/abs/1003.1294v1

Mathematics

Combinatorics

13 pages

Scientific paper

We study the arity gap of functions of several variables defined on an arbitrary set A and valued in another set B. The arity gap of such a function is the minimum decrease in the number of essential variables when variables are identified. We establish a complete classification of functions according to their arity gap, extending existing results for finite functions. This classification is refined when the codomain B has a group structure, by providing unique decompositions into sums of functions of a prescribed form. As an application of the unique decompositions, in the case of finite sets we count, for each n and p, the number of n-ary functions that depend on all of their variables and have arity gap p.

Affiliated with

Also associated with

No associations

Rating

Decompositions of functions based on arity gap does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Decompositions of functions based on arity gap, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Decompositions of functions based on arity gap will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-687929