Linear rank inequalities on five or more variables

Details Linear rank inequalities on five or more variables Linear rank inequalities on five or more variables

2009-10-02

arxiv.org/abs/0910.0284v3

Computer Science

Information Theory

Substantial improvements, including a stronger form of the second general construction of inequalities, many more six-variable

Scientific paper

Ranks of subspaces of vector spaces satisfy all linear inequalities satisfied by entropies (including the standard Shannon inequalities) and an additional inequality due to Ingleton. It is known that the Shannon and Ingleton inequalities generate all such linear rank inequalities on up to four variables, but it has been an open question whether additional inequalities hold for the case of five or more variables. Here we give a list of 24 inequalities which, together with the Shannon and Ingleton inequalities, generate all linear rank inequalities on five variables. We also give a partial list of linear rank inequalities on six variables and general results which produce such inequalities on an arbitrary number of variables; we prove that there are essentially new inequalities at each number of variables beyond four (a result also proved recently by Kinser).

Affiliated with

Also associated with

No associations

Rating

Linear rank inequalities on five or more variables 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 Linear rank inequalities on five or more variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Linear rank inequalities on five or more variables will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-25678