Patterns of Alternating Sign Matrices

Details Patterns of Alternating Sign Matrices Patterns of Alternating Sign Matrices

2011-04-20

arxiv.org/abs/1104.4075v2

Mathematics

Combinatorics

35 pages, 2 figures

Scientific paper

We initiate a study of the zero-nonzero patterns of n by n alternating sign matrices. We characterize the row (column) sum vectors of these patterns and determine their minimum term rank. In the case of connected alternating sign matrices, we find the minimum number of nonzero entries and characterize the case of equality. We also study symmetric alternating sign matrices, in particular, those with only zeros on the main diagonal. These give rise to alternating signed graphs without loops, and we determine the maximum number of edges in such graphs. We also consider n by n alternating sign matrices whose patterns are maximal within the class of all n by n alternating sign matrices.

Affiliated with

Also associated with

No associations

Rating

Patterns of Alternating Sign Matrices 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 Patterns of Alternating Sign Matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Patterns of Alternating Sign Matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-433509