부분순서

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  1. Then R is called a partial order relation, and the set S together with partial order is called a partially order set or POSET and is denoted by (S, ≤).[1]
  2. The set A is called linearly ordered set or totally ordered set, if every pair of elements in A is comparable.[1]
  3. The set of positive integers I + with the usual order ≤ is a linearly ordered set.[1]
  4. A partially ordered set is a set endowed with an ordering criterion, which is in general not complete, that is, such that some pairs of elements of the set cannot be ordered or compared.[2]
  5. A poset with a top element and bottom element is called bounded.[3]
  6. A poset with a bounding countable subset is called σ \sigma -bounded.[3]
  7. Note that every bounded poset is σ \sigma -bounded, but not conversely.[3]
  8. A poset can be understood as a (0,1)-category.[3]
  9. Given a partially ordered set, how hard is it to count the number of linear extensions?[4]
  10. If the order is total, so that no two elements of P are incomparable, then the ordered set is a totally ordered set .[5]
  11. If the order is partial, so that P has two or more incomparable elements, then the ordered set is a partially ordered set .[5]
  12. At the other extreme, if no two elements are comparable unless they are equal, then the ordered set is an antichain .[5]
  13. It is common for people to refer briefly though inaccurately to an ordered set as an order , to a totally ordered set as a total order , and to a partially ordered set as a partial order .[5]
  14. In a partially ordered set, it is not necessary that every pair of elements \(a\) and \(b\) be comparable.[6]
  15. A set together with a partial ordering is called a partially ordered set or poset.[7]
  16. The symbol is used to denote the relation in any poset.[7]
  17. Let and be the elements of a poset , then and are said to comparable if either or .[7]
  18. An element in the poset is said to be maximal if there is no element in the poset such that .[7]
  19. The digraph for a poset can be simplified.[8]
  20. The definition of a poset does not require every pair of distinct elements to be comparable.[8]
  21. The poset \((\mathbb{N},\leq)\) is a totally ordered set.[8]
  22. The poset \((\{1,5,25,125\},\mid)\) is also a totally ordered set.[8]
  23. Within a poset, there can be sequences of elements that are totally ordered, and these are called chains.[9]
  24. If the binary relation ⊵ is reflexive and antisymmetric, we say that (X, ⊵) is a pseudo-ordered set or a psoset.[10]
  25. Let (X, ⊵) be a nonempty pseudo-ordered set.[10]
  26. Let (X, ⊵) be a nonempty finite pseudo-ordered set.[10]
  27. Let (X, ≤) be a nonempty finite partially ordered set.[10]
  28. The natural mathematical home for the constant rate property is a partially ordered set (poset) with a reference measure for the density functions.[11]
  29. In spite of the minimal algebraic structure of a poset, there is a surprisingly rich theory, including moment results and results concerning ladder variables and point processes.[11]
  30. In many respects, constant rate distributions lead to the most random way to put ordered points in the poset.[11]
  31. The term standard poset will refer to a poset together with a measure space that satisfies the algebraic and measure theoretic assumptions.[11]
  32. Directed set; Lattice; Semi-lattice; Totally ordered set; Well-ordered set).[12]
  33. In the same work he defined the order type of a totally ordered set, that is, in modern terminology, the class of all totally ordered sets isomorphic to a given one.[12]
  34. Such a set is also called a Noetherian poset.[12]
  35. Then in the associated partially ordered set of equivalence classes, the set of minimal elements of each non-empty subset is non-empty and finite.[12]
  36. A partially ordered set ( T , ≥ ) , which could be the set inclusion order for binary images, the natural order of scalars for grey-scale images, and so on; 2.[13]
  37. In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.[14]
  38. A poset consists of a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other in the ordering.[14]
  39. The word partial in the names "partial order" and "partially ordered set" is used as an indication that not every pair of elements needs to be comparable.[14]
  40. That is, there may be pairs of elements for which neither element precedes the other in the poset.[14]
  41. A partially ordered set (or poset) is a set taken together with a partial order on it.[15]
  42. An element in a partially ordered set is said to be an upper bound for a subset of if for every , we have .[15]
  43. If there is an upper bound and a lower bound for , then the poset is said to be bounded.[15]

소스

  1. ↑ 1.0 1.1 1.2 Discrete Mathematics Partially Ordered Sets
  2. ↑ Partially Ordered Sets
  3. ↑ 3.0 3.1 3.2 3.3 partial order in nLab
  4. ↑ Partially Ordered Sets
  5. ↑ 5.0 5.1 5.2 5.3 Ordered Sets
  6. ↑ Partial Orders
  7. ↑ 7.0 7.1 7.2 7.3 Partial Orders and Lattices - GeeksforGeeks
  8. ↑ 8.0 8.1 8.2 8.3 7.4: Partial and Total Ordering
  9. ↑ Note (i) for Space, Time and Relativity: A New Kind of Science
  10. ↑ 10.0 10.1 10.2 10.3 The fixed point and the common fixed point properties in finite pseudo-ordered sets
  11. ↑ 11.0 11.1 11.2 11.3 Constant Rate Distributions on Partially Ordered Sets
  12. ↑ 12.0 12.1 12.2 12.3 Partially ordered set
  13. ↑ Partially Ordered Set - an overview
  14. ↑ 14.0 14.1 14.2 14.3 Partially ordered set
  15. ↑ 15.0 15.1 15.2 Partially Ordered Set -- from Wolfram MathWorld

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Spacy 패턴 목록

  • [{'LOWER': 'partially'}, {'LOWER': 'ordered'}, {'LEMMA': 'set'}]
  • [{'LEMMA': 'poset'}]
  • [{'LOWER': 'ordered'}, {'LEMMA': 'set'}]
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