Supnick matrix

A Supnick matrix or Supnick array is a Monge array which is symmetrical across its main diagonal.

Mathematical definition

A Supnick matrix must satisfy the requirements of a Monge array plus the requirements of symmetric arrays.

A Supnick matrix is an m-by-n matrix if, for all i, j, k, l such that

$1\leq i<k\leq m$ and $1\leq j<l\leq n$

one obtains

$A[i,j]+A[k,l]\leq A[i,l]+A[k,j]$

'and'

$a_{ij}=a_{ji}\,\!$

References

• 'Some problems around travelling salesmen, dart boards, and euro-coins' by Vladimir G. Deineko and Gerhard J. Woeginger, appeared in the Bulletin of the European Association for Theoretical Computer Science (EATCS), Number 90, October 2006, ISSN 0252-9742, page 44. See online edition (PDF).