  Motivated by the minimal tower problem, an earlier work studied
diagonalizations of covers where the covers are related to linear quasiorders
(tau-covers). We deal with two types of combinatorial questions which arise
from this study.
  1. Two new cardinals introduced in the topological study are expressed in
terms of well known cardinals characteristics of the continuum.
  2. We study the additivity numbers of the combinatorial notions corresponding
to the topological diagonalization notions.
  This gives new insights on the structure of the eventual dominance ordering
on the Baire space, the almost inclusion ordering on the Rothberger space, and
the interactions between them.
