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In mathematics, 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 that for every element x, all maximal chains among those with x as greatest element have the same finite length, or; a poset in which all maximal chains have the same ...
The rank is consistent with the covering relation of the ordering, meaning that for all x and y, if y covers x then ρ(y) = ρ(x) + 1. The value of the rank function for an element of the poset is called its rank. Sometimes a graded poset is called a ranked poset but that phrase has other meanings; see Ranked poset.
In this poset, 60 is an upper bound (though not a least upper bound) of the subset {,,,}, which does not have any lower bound (since 1 is not in the poset); on the other hand 2 is a lower bound of the subset of powers of 2, which does not have any upper bound. If the number 0 is included, this will be the greatest element, since this is a ...
A poster of Le Chat Noir may also be seen prominently in the movie Breakfast at Tiffany's hanging on the wall over the staircase. Le Chat Noir is the name of the nightclub where Frank Sinatra and Natalie Wood rekindle their relationship, in the 1958 movie Kings Go Forth. There is also the famous cat painting with blinking eyes on the entrance wall.
A k-Sperner poset is a graded poset in which no union of k antichains is larger than the union of the k largest rank levels, [1] or, equivalently, the poset has a maximum k-family consisting of k rank levels. [2] A strict Sperner poset is a graded poset in which all maximum antichains are rank levels. [2]
An Eulerian poset which is a lattice is an Eulerian lattice. These objects are named after Leonhard Euler . Eulerian lattices generalize face lattices of convex polytopes and much recent research has been devoted to extending known results from polyhedral combinatorics , such as various restrictions on f -vectors of convex simplicial polytopes ...
Thé Matcha 26 Eau de Parfum. Everyone loved the fig/tea vibes of Thé Noir so much that Le Labo developed Thé Matcha, a fig/matcha fragrance. But to me, it's kind of like if every single Le Labo ...
In mathematics, specifically category theory, a posetal category, or thin category, [1] is a category whose homsets each contain at most one morphism. [2] As such, a posetal category amounts to a preordered class (or a preordered set, if its objects form a set).