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2. Partially ordered set - Wikipedia

   en.wikipedia.org/wiki/Partially_ordered_set

   A partially ordered set (poset for short) is an ordered pair = (,) consisting of a set (called the ground set of ) and a partial order on . When the meaning is clear from context and there is no ambiguity about the partial order, the set X {\displaystyle X} itself is sometimes called a poset.

3. Deviation of a poset - Wikipedia

   en.wikipedia.org/wiki/Deviation_of_a_poset

   The poset of positive integers has deviation 0: every descending chain is finite, so the defining condition for deviation is vacuously true. However, its opposite poset has deviation 1. Let k be an algebraically closed field and consider the poset of ideals of the polynomial ring k[x] in one variable. Since the deviation of this poset is the ...

4. Glossary of set theory - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_set_theory

   2. An inductive definition is a definition that specifies how to construct members of a set based on members already known to be in the set, often used for defining recursively defined sequences, functions, and structures. 3. A poset is called inductive if every non-empty ordered subset has an upper bound infinity axiom See Axiom of infinity.

5. Data conversion - Wikipedia

   en.wikipedia.org/wiki/Data_conversion

   For example, a word processor may convert an RTF file to a WordPerfect file by converting the RTF to OpenDocument and then that to WordPerfect format. An image conversion program does not convert a PCX image to PNG directly; instead, when loading the PCX image, it decodes it to a simple bitmap format for internal use in memory, and when ...

6. Order dimension - Wikipedia

   en.wikipedia.org/wiki/Order_dimension

   Thus, an equivalent definition of the dimension of a poset P is "the least cardinality of a realizer of P." It can be shown that any nonempty family R of linear extensions is a realizer of a finite partially ordered set P if and only if, for every critical pair ( x , y ) of P , y < i x for some order < i in R .

7. Incidence poset - Wikipedia

   en.wikipedia.org/wiki/Incidence_poset

   In mathematics, an incidence poset or incidence order is a type of partially ordered set that represents the incidence relation between vertices and edges of an undirected graph. The incidence poset of a graph G has an element for each vertex or edge in G ; in this poset, there is an order relation x ≤ y if and only if either x = y or x is a ...