# Tagged Questions

**3**

votes

**1**answer

101 views

### For what classes of comparability graphs are their complements also comparability graphs?

An interval graph is an intersection graph of real intervals, that is, an undirected graph whose vertices can be labeled with real intervals so that there is an edge between two vertices iff their ...

**1**

vote

**0**answers

84 views

### Set of upper bounds is finite for any finite subset

Is there a term to describe a preordered set $P$ in which any finite subset $S \subset P$ has at most finitely many minimal upper bounds? The preordered sets I'm studying generally aren't ...

**6**

votes

**1**answer

218 views

### Is it possible to decide in polynomial time if a poset is a subposet of another which is given ?

I am reading some theory on partial orders and I wonder something which perhaps has a simple answer : Given two partial orders $G_1,G_2$ (by their hasse diagrams), is it possible to know in ...

**0**

votes

**0**answers

207 views

### Transitive closures and inductive reasoning [solved]

Let's say that r is an endorelation over A (i.e. $r$ is a subset of $A \times A$), $\bar{r}$ is the transitive closure of r (i.e. the least set containing r and being transitive).
Furthermore $r$ has ...

**1**

vote

**0**answers

216 views

### Modern books about orders and algebras on trees

Please help to find books about orders and algebras on trees.
If there is no modern books, please advice good old ones!
I'm more interested in finite trees (my current problem), but infinite ones are ...

**14**

votes

**3**answers

798 views

### Subposets of small Dushnik-Miller dimension

The Dushnik–Miller dimension of a partial order $(P,{\leq})$ is the smallest possible size $d$ for a family ${\leq_1},\ldots,{\leq_d}$ of total orderings of $P$ whose intersection is ${\leq}$, ...

**23**

votes

**9**answers

2k views

### How many groups of size at most n are there? What is the asymptotic growth rate? And what of rings, fields, graphs, partial orders, etc.?

Question. How many (isomorphism types of) finite groups of size at most n are there? What is the asymptotic growth rate? And the same question for rings,
fields, graphs, partial orders, etc.
...

**3**

votes

**3**answers

217 views

### Name for “lower/upper bounds” of arbitrary relations?

Given a partial order $R_{\leq}$ over a set $D$, the set of upper bounds under $R$ of a subset $S$ of $D$ is commonly defined as $\{ y \in D | \ \forall x\in S, x R y \}$.
(The set of lower bounds of ...

**3**

votes

**2**answers

561 views

### Reconstruction puzzles

[Added: This is a follow-up of an earlier post.]
Consider the following "reconstruction puzzle", stated informally:
Given a concrete poset, e.g. the poset of undirected unlabeled finite graphs ...