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Questions tagged [poset]

POSet in a shorthand for Partially Ordered Set, that is a Set with a Partial Order.

A partial order is a binary relation ≤ over a set P which is reflexive, antisymmetric, and transitive, i.e., which satisfies for all a, b, and c in P:

  • a ≤ a (reflexivity);
  • if a ≤ b and b ≤ a then a = b (antisymmetry);
  • if a ≤ b and b ≤ c then a ≤ c (transitivity).

A POSet is just a set with a partial order.

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How to represent a binary relation

I plan to make a class that represents a strict partially ordered set, and I assume the most natural way to model its interface is as a binary relation. This gives functions like: bool test(elementA, elementB); //return true if elementA <…
Brent
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Probability of an element of a poset being the maximum?

Given a partially-ordered set (poset), what is an algorithm for estimating the probability of an element being top-most in a linear extension, assuming that all linear extensions are equally likely?
alltom
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Creating Class relation

Given an array of modules, what is the best way to return an array that describes the normalized (minimal) ordering relations between the modules? Each element of the array should be an array of pairs of modules that have child-parent relation. The…
sawa
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Algorithm for constructing Hasse Diagram

Please help me in improving the time complexity of the following algorithm. Hasse Diagram(Skip this section if you already know what is Hasse Diagram, Please directly go to next section): Consider a partially ordered set (poset, for short) (A,⊆),…
algo_freek
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Poset iteration order / custom iterator implementation for a partially ordered set

I am creating a partially ordered set as an abstract data type in java, and I have to make an iterator version of the set of numbers, and an iterator for the relations. Now for the elements, I've used HashSet of integer, and for the relations, I've…
hakuna matata
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How to compose two partial orders in Sage?

Suppose I have two finite posets (e.g. constructed with sage.combinat.posets.posets.FinitePoset). I want to calculate the binary relation which is the composition of the order relations of these posets. How to do this in Sage? (I am a Sage novice.)
porton
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poset iteration implementation correctness

I wrote a custom iterator class that iterates over the set of numbers found in a PoSet, and here is my code: private class IntGenerator implements Iterator { private Iterator i; private Set returnedNumbers; …
hakuna matata
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Algorithm to generate a lattice (Poset) from a positive integer parameter

As the title suggests, I've been trying to create a lattice (Poset) generator from a positive integer parameter n which represents the number of nodes. The reason why I'm trying to do this is because I want to create hasse diagrams of lattices for…
Luisz
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How to identify and plot partial order on dummy variables in R (ideally tidyverse)

I have a system of n dummy variables/set indicators. I want to automatically identify any nesting. Take a simple n = 3 case. expand.grid(0:1, 0:1, 1) Var1 Var2 Var3 0 0 1 1 0 1 0 1 1 1 1 1 E.g. Here Var1 and Var2 are not…
JRC
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Java Poset simulation

I'm looking to simulate a poset, called x say, of size 2n in java of the form a_1 < a_2 < ... < a_n, and b_1 < b_2 < ... < b_n. I want to run an iteration to get a random linear extension whereby I compare the 'size' of each object and if two…
user528676
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What is transitivity property of digraph?

I'm studying discrete structures following the MIT lecture (Mathematics for Computer Science). In the book, the definition of transitivity is as follow: Then the book says the graph in Figure 7.8 below does not satisfy the transitivity…
Stone
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partial order - finite set - minimal element

Prove by induction.Every partial order on a nonempty finite set at least one minimal element. How can I solve that question ?
user478571
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Computing the maximum antichain when incomparability relations are given as LinkedHashMap

I am trying to compute the maximum antichain for a given poset. I have created the following method: public boolean isIncomparable(Node a,Node b) { if(isReachable(a,b)||isReachable(b,a)) return false; return true; } which returns…
seteropere
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