**2**

votes

**1**answer

273 views

### Count of lattices on finite set

Let $p(n)$ denote count of lattices on finite set $G$, $|G|=n$ (without isomorphism). It's know closed formula for $p(n)$?
It's clear, that $1 \leq p(n)$ and also that $p(n-1) \leq p(n)$ for $n \geq ...

**3**

votes

**1**answer

286 views

### Posets of finite sequences are highly connected

I need the following result for an example in a paper I'm writing. It's easy enough to prove, but I'd prefer to just give a reference. Does anyone know one?
Fix $1 \leq k \leq n$. Define $X_{n,k}$ ...

**3**

votes

**0**answers

337 views

### a poset with small “cycles”

(a followup to this recent question)
I noticed the following curious property of a poset (which I strongly believe to be a lattice, I'm still trying to prove that...):
Suppose that $z$ is covered by ...

**14**

votes

**3**answers

2k views

### Proving that a poset is a lattice

I discovered experimentally that a certain finite poset (sorry, I cannot give its definition here) seems to be in fact a (non-distributive, non-graded) lattice. The covering relations are reasonably ...

**7**

votes

**2**answers

356 views

### A sequence of generic filters that does not come from an iteration

Fix a countable transitive model $M$ of ZFC.
In my answer to this question I indicated that there are forcing iterations
$((Q_\alpha:\alpha\leq\omega),(\dot P_\alpha:\alpha<\omega))$ in $M$ and ...

**13**

votes

**3**answers

1k views

### Banach and Knaster-Tarski fixed point theorems — are they related?

It there any known way of obtaining the Banach fixed-point theorem from the Tarski fixed-point theorem or vice-versa?

**2**

votes

**1**answer

253 views

### Selecting k sub-posets

I ran into the following algorithmic problem while experimenting with classification algorithms. Elements are classified into a polyhierarchy, what I understand to be a poset with a single root ...

**48**

votes

**6**answers

10k views

### How many orders of infinity are there?

Define a growth function to be a monotone increasing function $F: {\bf N} \to {\bf N}$, thus for instance $n \mapsto n^2$, $n \mapsto 2^n$, $n \mapsto 2^{2^n}$ are examples of growth functions. Let's ...

**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 ${\leq}$, ...

**2**

votes

**0**answers

119 views

### non-degenarete tools to calculate a derived functor on a model category which is a poset?

Are there theorems (esp. computational tools) on model categories which survive and do not trivialise when its underlying category is a (quasi-)poset ? Are there tools
that may help to calculate ...

**1**

vote

**2**answers

828 views

### Proof of glb and lub of Lexicographic Product of poset

Is there a book, or a paper where the Lexicographic glb and lub are proven commutative, associative, idempotent and absorbing. I have already proven this, but would like to check proofs, and a short ...

**4**

votes

**4**answers

752 views

### Category = Groupoid x Poset?

Is it possible to split a given category $C$ up into its groupoid of isomorphisms and a category that resembles a poset?
"Splitting up" should be that $C$ can be expressed as some kind of extension ...

**5**

votes

**3**answers

1k views

### Constructing a metric over a lattice

Consider a lattice $({\cal L}, \wedge, \vee)$ with an antimonotonic function $f: {\cal L} \rightarrow {\mathbb R}$ defined on it (i.e $x \preceq y \implies f(x) \ge f(y)$).
$f$ is said to be ...

**7**

votes

**1**answer

482 views

### Does ⋄ generate all De Morgan algebras?

(Asked by Nathaniel Hellerstein on the Q&A board at JMM)
This question is about De Morgan algebras (see also Wikipedia), which are something like Boolean algebras, but with a different weaker ...

**4**

votes

**2**answers

419 views

### Is every lattice the fixed-point set of an order endomorphism of ⋄^n?

(Asked by Nathaniel Hellerstein on the Q&A board at JMM)
Let ⋄ be the 4 element lattice
τ
/ \
i j
\ /
f
Is every lattice isomorphic to the fixed point lattice of some ...