English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Let R and S be two vectors of real numbers whose entries have the same sum.In the transportation problems one wishes to find a matrix A with row sumvector R and column sum vector S. If, in addition, the two vectors only containnonnegative integers then one wants the same to be true for A. This can alwaysbe done and the transportation algorithm gives a method for explicitlycalculating A. We can restrict things even further and insist that A have onlyentries zero and one. In this case, the Gale-Ryser Theorem gives necessary andsufficient conditions for A to exist and this result can be provedconstructively. One can let the dihedral group D_4 of the square act onmatrices. Then a subgroup of D_4 defines a set of matrices invariant under thesubgroup. So one can consider analogues of the transportation and (0,1)problems for these sets of matrices. For every subgroup, we give conditionsequivalent to the existence of the desired type of matrix.

Dihedral Transportation and (0,1)-Matrix Classes