All Questions
Tagged with order-theory reference-request
108
questions
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40
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List of all posets of size $n$ for small $n$? [duplicate]
Is there a good reference for, or an easy way of generating, all Hasse diagrams of partially ordered sets of small size (say $n\leq 6$)? I am familiar with the OEIS entry A000112 listing the number of ...
- 1,307
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20
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Optimization of totally ordered set valued function.
I am familiar with the meaning of optimizing a function $f : \Omega \to \mathbb{R+}$. However I was just wondering if there's some theory of math explaining how to optimize mapping from $f : \Omega \...
- 5,317
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28
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Relabel According to the Order of First Occurrence
Let $a\in\mathbb R^n$ be a tuple of length $n\in\mathbb Z_{>0}$. Let $X=\{a_i:1\le i\le n\}$ be the set of elements of $a$. For $x\in X$ let
$$i(x)=\min\{j:a_j=x\}$$
be the first occurence of $x$ ...
- 3,633
2
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35
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Number of partial orders such that a given function is monotone (order homomorphism)?
Given a set $X$, a poset $(Y, \preceq)$, and an arbitrary function $f: X \to Y$, how many partial orders $\le$ can one construct on $X$ such that $f$ becomes an order homomorphism $(X, \le) \to (Y, \...
- 1,458
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34
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Ultraproduct with respect to a partially ordered set
I am interested in learning about limits with respect to ultrafilters on a poset (partially ordered set) and ultraproducts with respect to a poset. However, all I can find about this topic only ...
- 489
1
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35
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Will this attempt to mathematically formalize the Burrows Wheeler Transform (BWT) let us define generalizations or variations of it?
Background: The Burrows-Wheeler Transform (BWT) is an a mathematical transform traditionally defined on strings of letters and used in signal processing for example for data compression purposes.
Here ...
- 26.1k
2
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41
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Every bounded monotone sequence converges, most general version
It is a well known fact that in many contexts, every bounded monotone sequence converges.
I wonder what is the most general context where this happens. That is,
Let $X$ be a set equipped with a ...
- 8,127
3
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62
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On the transitivity of the Löwner order
If the Löwner order is a partial order, then it is transitive. If so, how can one prove it?
Proposition. Let ${\Bbb S}_n ({\Bbb R})$ denote the set of $n \times n$ symmetric matrices over $\Bbb R$. ...
0
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22
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Is this property equivalent to the antisymmetric property for relations?
I was trying to prove that a certain relation ($\leq$) in a real vector space is a partial order, and I lack the antisymmetric property. However, I have been able to prove the following statement:
If $...
- 323
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55
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Is there a commonly used name for this weakening of the Archimedean property?
Suppose that $R$ is a partially ordered commutative ring.
The order behaves nicely: We have $0 \leq 1$. If $a \leq b$ and $c > 0$, then $a + c \leq b + c$ and $a \cdot c \leq b \cdot c$.
For $n \in ...
- 3,882
1
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1
answer
114
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Database of lattices and lattice properties
Are there any websites that are databases of lattices?
I'm also interested in databases distributed as libraries in a programming language or similar.
I'm studying a little bit of lattice theory on ...
- 11.9k
5
votes
1
answer
74
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Two poset properties: are they related?
A bunch of infinite posets $P$ with $\hat 0$ have the following property
For every $x\in P$, the principal filter $\{ y\in P : y\ge x\}$ is isomorphic as a poset to $P$ itself.
Examples include ${\...
- 1,794
4
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1
answer
245
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Definition of an interval in a poset
I can think of two nonequivalent ways of defining an interval in a poset:
An interval of a poset $P$ is a subset $I\subset P$ with the property that for all $x, y, z\in P$ such that $x < y < z$ ...
- 2,210
2
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51
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Reference for Jech's notion of stationary set
I am writing a brief introduction to the Proper Forcing Axiom and I need a reference for Jech's notion of stationary set in $[\lambda]^\omega$ : https://en.wikipedia.org/wiki/Stationary_set#Jech'...
- 566
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1
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159
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On the existence of a totally ordered set in a partially ordered set.
I can't find references regarding the following problem, could someone give me some suggestions or information?
From any partially ordered set we can extract a totally ordered set.
Definition$(\text{...
- 162