- Mirsky's
theorem the
minimum number of
antichains into
which the set can be partitioned. The
family of all
antichains in a
finite partially ordered set can...
-
common lower bound. Thus
lattices have only
trivial strong antichains (i.e.,
strong antichains of
cardinality at most 1). Kunen,
Kenneth (1980), Set Theory:...
-
maximal simplices in a
complex form an
antichain. For n = 2,
there are six
monotonic Boolean functions and six
antichains of
subsets of the two-element set...
- have
equal values of N, is an
antichain, and
these antichains partition the
partial order into a
number of
antichains equal to the size of the largest...
- have
equal values of N, is an
antichain, and
these antichains partition the
partial order into a
number of
antichains equal to the size of the largest...
-
satisfy the
countable chain condition, or to be ccc, if
every strong antichain in X is countable.
There are
really two conditions: the
upwards and downwards...
- numbers:
number of
monotone Boolean functions of n variables,
number of
antichains of
subsets of an n-set,
number of
elements in a free
distributive lattice...
- then the
subsets with
equal labels form a
partition into
antichains, with the
number of
antichains equal to the size of the
largest chain overall. Every...
-
efficient analysis may be
obtained by
abstracting sets of
cache states by
antichains which are
represented by
compact binary decision diagrams. LRU static...
- The
importance of
antichains in
forcing is that for most purposes,
dense sets and
maximal antichains are equivalent. A
maximal antichain A {\displaystyle...
