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  2. Ranked poset - Wikipedia

    en.wikipedia.org/wiki/Ranked_poset

    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 ...

  3. Graded poset - Wikipedia

    en.wikipedia.org/wiki/Graded_poset

    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.

  4. Sperner property of a partially ordered set - Wikipedia

    en.wikipedia.org/wiki/Sperner_property_of_a...

    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]

  5. Partially ordered set - Wikipedia

    en.wikipedia.org/wiki/Partially_ordered_set

    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".

  6. List of IRC commands - Wikipedia

    en.wikipedia.org/wiki/List_of_IRC_commands

    This is a list of all Internet Relay Chat commands from RFC 1459, RFC 2812, and extensions added to major IRC daemons. Most IRC clients require commands to be preceded by a slash (" / "). Some commands are actually sent to IRC bots ; these are treated by the IRC protocol as ordinary messages, not as / -commands.

  7. Markets stumble as Wall Street sells off Big Tech - AOL

    www.aol.com/dow-tumbles-500-points-wall...

    US stocks ended Friday in the red, closing out a lackluster week despite a year of historic highs. The “Magnificent Seven” group of high-performing tech stocks — Alphabet, Amazon, Apple ...

  8. Luigi Mangione was indicted in New York over United Health ...

    www.aol.com/news/luigi-mangione-indicted-york...

    Luigi Mangione, the suspect in the murder of UnitedHealthcare CEO Brian Thompson, faces 11 separate charges in New York, including two terrorism-related counts, Manhattan District Attorney Alvin ...

  9. ChatScript - Wikipedia

    en.wikipedia.org/wiki/ChatScript

    Some data in ChatScript is transient, meaning it will disappear at the end of the current volley. Other data is permanent, lasting forever until explicitly killed off. Data can be local to a single user or shared across all users at the bot level. Internally all data is represented as text and is automatically converted to a numeric form as needed.