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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 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. A rank or rank level of a graded poset is the subset of all the elements of the poset that have a given rank value. [1] [2]
A convex set in a poset P is a subset I of P with the property that, for any x and y in I and any z in P, if x ≤ z ≤ y, then z is also in I. This definition generalizes the definition of intervals of real numbers. When there is possible confusion with convex sets of geometry, one uses order-convex instead of "convex".
Well, the good news is Andreessen Horowitz just released its third installment of Top 100 Gen AI Consumer Apps, which rounds up the most-used apps in the space. It's an excellent way to find some ...
Most commonly, the meaning of "DW" in text is "don't worry." (Doctor Who or Arthur fans everywhere may disagree.) This meaning applies to social media platforms such as Facebook and Instagram as well.
Comparison of user features of messaging platforms refers to a comparison of all the various user features of various electronic instant messaging platforms. This includes a wide variety of resources; it includes standalone apps, platforms within websites, computer software, and various internal functions available on specific devices, such as iMessage for iPhones.
In mathematics, the poset topology associated to a poset (S, ≤) is the Alexandrov topology (open sets are upper sets) on the poset of finite chains of (S, ≤), ordered by inclusion. Let V be a set of vertices. An abstract simplicial complex Δ is a set of finite sets of vertices, known as faces , such that
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