Weak-join of matriods
Weighted Aztec diamond graphs and the Weyl character formula.
When can you tile a box with translates of two given rectangular bricks?
When does the inverse have the same sign pattern as the transpose?
By a sign pattern (matrix) we mean an array whose entries are from the set . The sign patterns for which every real matrix with sign pattern has the property that its inverse has sign pattern are characterized. Sign patterns for which some real matrix with sign pattern has that property are investigated. Some fundamental results as well as constructions concerning such sign pattern matrices are provided. The relation between these sign patterns and the sign patterns of orthogonal matrices...
When is a 0-1 knapsack a matroid?
When is an Incomplete 3 × n Latin Rectangle Completable?
We use the concept of an availability matrix, introduced in Euler [7], to describe the family of all minimal incomplete 3 × n latin rectangles that are not completable. We also present a complete description of minimal incomplete such latin squares of order 4.