Antichain and Partially ordered set

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Difference between Antichain and Partially ordered set

Antichain vs. Partially ordered set

In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two distinct elements in the subset are incomparable. 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.

Similarities between Antichain and Partially ordered set

Antichain and Partially ordered set have 7 things in common (in Unionpedia): Birkhoff's representation theorem, Comparability, Distributive lattice, Mathematics, Order theory, Subset, Total order.

Birkhoff's representation theorem

In mathematics, Birkhoff's representation theorem for distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in such a way that the lattice operations correspond to unions and intersections of sets.

Antichain and Birkhoff's representation theorem · Birkhoff's representation theorem and Partially ordered set · See more »

Comparability

In mathematics, any two elements x and y of a set P that is partially ordered by a binary relation ≤ are comparable when either x ≤ y or y ≤ x. If it is not the case that x and y are comparable, then they are called incomparable.

Antichain and Comparability · Comparability and Partially ordered set · See more »

Distributive lattice

In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Order theory

Order theory is a branch of mathematics which investigates the intuitive notion of order using binary relations.

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Subset

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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Total order

In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set X, which is antisymmetric, transitive, and a connex relation.

Antichain and Total order · Partially ordered set and Total order · See more »

The list above answers the following questions

What Antichain and Partially ordered set have in common
What are the similarities between Antichain and Partially ordered set

Antichain and Partially ordered set Comparison

Antichain has 15 relations, while Partially ordered set has 98. As they have in common 7, the Jaccard index is 6.19% = 7 / (15 + 98).

References

This article shows the relationship between Antichain and Partially ordered set. To access each article from which the information was extracted, please visit:

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