All Questions
Tagged with lattice-orders reference-request
57
questions
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29
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Reference for quotient lattices and universal property?
Question: Are there any references explaining the definition (or definitions) of quotient objects in the category of lattices?
In particular a characterization in terms of universal properties would ...
- 1,458
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0
answers
70
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Lattices/Topology and the Stone Duality
For some context I have some partial understanding of lattices and an intermediate understanding of topology.
I at some point in the past week started thinking about a funny way to view a topology on ...
- 61
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20
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Lift and frame matroids.
I want to read more about lift matroid and frame matroid and their flats and relations to signed graphs, do you know any basic resources for this?
- 2,087
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Applications of a theorem of M. H. Stone to general topology
Exercise 2.I of J. Kelley's book General Topology introduces a theorem by M.H. Stone concerning maximal ideals in distributive lattices. The statement is the following :
Let $A$ and $B$ be disjoint ...
- 35.3k
1
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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
4
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answer
113
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Are there $N_n$ lattices generalizing the $N_5$ lattice?
$M_3$ and $N_5$ lattice, respectively, is a widely used notation for these two lattices.
I'm wondering what the indices mean.
For the M case, I found in the book of B. A. Davey, H. A. Priestley, ...
- 4,307
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26
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Generalizing section-based operations on abstract polytopes
While writing some code to explore abstract polytopes, I've noticed that many intuitive polytope operations (like the Conway polyhedron operations) can be obtained by defining the output polytope $Q$ ...
- 11.8k
6
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The lattices $M_3$ and $N_5$
Why are $M_3$ and $N_5$ lattices in the theory of lattices called so?
They are well known for that their existence as a sublattice signifies lack of modularity/distributivity, yet their names are a ...
- 10.5k
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151
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A cartesian product of distributive lattices is distibutive
I have seen a few articles cite this result as coming from the 3rd edition of G Birkhoff's "Lattice theory" but I can't find the result in there myself.
The index does not seem to mention &...
- 469
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3
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193
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Determining if lattice elements are equal
I am working in a distributive lattice with top and bottom elements.
I would like to know if there is an algorithm to determine if $s=t$ for any two elements $s,t$ in the lattice. For example, if $t=s\...
- 369
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159
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On the existence of a totally ordered set in a partially ordered set.
I can't find references regarding the following problem, could someone give me some suggestions or information?
From any partially ordered set we can extract a totally ordered set.
Definition$(\text{...
- 162
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Reference request: finding maximal ordered subgroups of lattice-ordered groups?
I am trying to find references that provide techniques for constructing (totally-) ordered subgroups of lattice-ordered groups $G$. For those who are not familiar, a lattice-ordered group $G$ is set ...
1
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0
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A general setting to state the isomorphism theorems for (complete) (semi)lattices
Lattices, complete lattices and (complete) lower and upper semilattices are all very similar algebraic structures. The homomorphisms between lattices of the same type and also the Isomorphism Theorems ...
- 355
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44
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Is the set of noncrossing partitions of an infinite set a lattice?
It is well-known that the set of noncrossing partitions of a finite set is a lattice;
see e.g. Wikipedia or the 1991 article by Simion and Ullman.
What about the infinite case?
Is the set of ...
- 1,148
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Does this lattice construction have a name?
Suppose we are given complete lattices $(L_i,\le_i)$ indexed over some set $I$, such that $L_i\ne 2$ and $L_i\cap L_j=\emptyset$ for all $i\ne j$. There is a sort of "amalgamation" that can ...
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