- that is reflexive, antisymmetric, and transitive. A
partially ordered set (
poset for short) is an
ordered pair P = ( X , ≤ ) {\displaystyle P=(X,\leq )}...
- In mathematics, the
poset topology ****ociated to a
poset (S, ≤) is the
Alexandrov topology (open sets are
upper sets) on the
poset of
finite chains of...
-
Eulerian poset is a
graded poset in
which every nontrivial interval has the same
number of
elements of even rank as of odd rank. An
Eulerian poset which...
- sets is open.
Algebraic poset. A
poset is
algebraic if it has a base of
compact elements. Antichain. An
antichain is a
poset in
which no two elements...
- mathematics, in the
branch of combinatorics, a
graded poset is a partially-ordered set (
poset) P
equipped with a rank
function ρ from P to the set N...
- a
ranked poset is a
partially ordered set in
which one of the
following (non-equivalent)
conditions hold: it is a
graded poset, or a
poset with the property...
- S2CID 38115497. Ganapathy,
Jayanthi (1992). "Maximal
Elements and
Upper Bounds in
Posets". Pi Mu
Epsilon Journal. 9 (7): 462–464. ISSN 0031-952X. JSTOR 24340068...
-
pointed dcpos as
posets in
which every chain has a supremum. A
related notion is that of ω-complete
partial order (ω-cpo).
These are
posets in
which every...
-
generating functions used in
combinatorics and
number theory. A
locally finite poset is one in
which every closed interval [a, b] = {x : a ≤ x ≤ b} is finite...
- In mathematics, the
power set (or powerset) of a set S is the set of all
subsets of S,
including the
empty set and S itself. In
axiomatic set
theory (as...
