Gale–Ryser Binary Matrix Margins

Turn row and column sums into sharp feasibility inequalities for binary matrices.

Experiment

In the Gale–Ryser Binary Matrix Margins module, you can explore whether a binary matrix can be formed with given margins:

1. Set Margins to "Equal total impossible".
2. Observe that the Status is "Inequality violation", even though the row and column totals are equal.
3. Look at the chart and see the red row sum line crosses above the blue capacity curve, showing at which k the violation occurs.
4. Switch Transpose to "Yes" and note how the first violated k changes.