Mass-scale red blood cell genotyping of donors and transfusion recipients increases the availability extended antigen matched units. Therefore, a new mathematical framework is developed that can be applied for general groups (i.e., beyond ABO, RhD groups). It determines which units should issued from inventory, such requests hospitals satisfied with compatible units, shortages future are avoide...

This paper is centered on the notion of interval order as a model for preferences. We introduce a family of representation languages for such orders, parameterized by a scale and an aggregation function. We show how interval orders can be represented by elements of those languages, called weighted bases. We identify the complexity of the main decision problems.

A result of Robinson states that no OD(n; 1, 1, 1, 1, 1, n− 5) exists for n > 40. We complement this result by showing the existence of OD(n; 1, 1, 1, 1, 1, n− 5) for n = 32, 40. This includes a resolution to an old open problem regarding orthogonal designs of order 32 as well. We also obtain a number of new orthogonal designs of order 32.

We study two partial orders on [x1, . . . , xn], the free abelian monoid on {x1, . . . , xn}. These partial orders, which we call the “strongly stable” and the “stable” partial order, are defined by the property that their filters are precisely the strongly stable and the stable monoid ideals. These ideals arise in the study of generic initial ideals.

Stȩpniak [Linear Algebra Appl. 151 (1991)] considered the problem of equivalence of the Löwner partial order of nonnegative definite matrices and the Löwner partial order of squares of those matrices. The paper was an important starting point for investigations of the problem of how an order between two matrices A and B from different sets of matrices can be preserved for the squares of the cor...