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May
29 |
comment |
Equality-preserving embeddings of finite trees
I don't understand your question. Isn't it true that every finite subset of the natural numbers is a special case of a finite set? |
May
17 |
awarded | Yearling |
May
8 |
comment |
Galois Connections: algorithmic generation
You are welcome. Today I got a literature suggestion about this topic (see edit). |
May
8 |
revised |
Galois Connections: algorithmic generation
Added an article suggestion |
May
3 |
answered | Galois Connections: algorithmic generation |
Mar
22 |
answered | Has the single sorted case of formal concept analysis been investigated? |
Jan
17 |
revised |
What is known about orbifolding ordered groups and sets? Who has been involved? Links to Lee metrics?
Added a further explanation to the question. |
Jan
17 |
awarded | Commentator |
Jan
17 |
comment |
What is known about orbifolding ordered groups and sets? Who has been involved? Links to Lee metrics?
A better description of $Λ$ would be: It describes the action that is necessary to map a tuple into the transversal if its first place is already there. |
Jan
17 |
awarded | Student |
Sep
18 |
comment |
Does the notion of graphs with vertex multiplicity exist?
A similar construction has been called binary relation orbifold (Borchmann, Daniel: Context Orbifolds, Diploma Thesis, TU Dresden, 2009, link). |
Sep
17 |
comment |
Conditions for a group to be lattice-ordered
I think you should contact one of the authors of the corresponding papers and ask them if they can help you. It is a very special branch of mathematics and propably of the contributers are not active participants of MO. |
Sep
15 |
comment |
Conditions for a group to be lattice-ordered
@BorisNovikov Have a look at my answer, Statement 1 (it was added before I saw your comment). The linear order that you constructed using Szpilrajn's lemma does not fulfil Xodaraps conditions. Thus, it is not a counterexample. |
Sep
15 |
answered | Conditions for a group to be lattice-ordered |
Sep
15 |
comment |
Conditions for a group to be lattice-ordered
The first implication in the proof of 2) does not hold. As in any right-ordered group the implications $x≤y ⇒ xz≤yz$ holds but not necessarily $x≤y⇒zx≤zy$. On the other hand Szpilrajn is not enough to construct a contradiction as $(\mathbb Z,≤)×(\mathbb Z,≤)$ has also linear order extension $≤_l$ that leads to $(x∨_ly)z=yz≠xz=xz∨_lyz$ for some $x,y,z$. |
Sep
14 |
comment |
Conditions for a group to be lattice-ordered
Is every right-ordered group with a lattice order already an ordered group? If not there are counterexamples as the implications $x≤1 ⇒ xz≤z$ and similarly for $x≥1$ is a conclusion of being right-ordered. Otherwise it would be sufficient to prove that it is a right-ordered group. |
Sep
13 |
revised |
Self-containing graphs
Some further consideration of loops. |
Sep
13 |
comment |
Self-containing graphs
If $H$ is a proper subgraph of some finite graph $G$ then $G$ there is no injective mapping from the set of nodes of $G$ into the set of nodes of $H$. |
Sep
12 |
revised |
Self-containing graphs
forgot to consider loops |
Sep
12 |
answered | Self-containing graphs |