Questions tagged [partial-order]

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How to prove substring is a partial order

u is defined to be a substring of a string v if v = xuy for some string x and y. Either or both possibly empty. How to you prove that a substring relation on any set of strings is a partial order?
0
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1answer
157 views

trouble with bijection definition [closed]

I have a bijection problem that I cannot get my head around. It goes like this: let f: A -> B and g: B -> C be functions such that g o f is a bijection. Prove that f must be one-to-one and that g ...
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3answers
5k views

Maintaining an efficient ordering where you can insert elements "in between" any two other elements in the ordering?

Imagine I have an ordering on a bunch of elements like so: Where an arrow $X \leftarrow Y$ means $X < Y$. It is also transitive: $\left(X < Y\right) \wedge \left(Y < Z\right) \implies \left(...
6
votes
1answer
112 views

Extracting the set of chains from a partial order

Given a partial ordered set (poset) $S$, is there a known procedure or algorithm to find the set of chains (i.e. subsets of $S$ where every two elements are comparable)? Note: I am asking here ...
2
votes
1answer
170 views

Is there an efficient method to store large DAGs?

I have a DAG representing strict partial order where each node is an assignment of variables $V$ to their values $v$. Each arc $(u,w)$ represents a change in one variable value such that $u\succ w$. ...
1
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2answers
236 views

Are these two relations on integers partial orders?

Are the following relations $R_1$ and $R_2$ defined on the set $\mathbb{Z}$ of integers partial orders? (A partial order is reflexive, antisymmetric and transitive.) $a$ $R_1$ $b$ if and only if $a = ...
3
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2answers
320 views

Given many partial orders, check them for consistency and report any that are not consistent

Inputs. I am given a finite set $S$ of symbols. I know there should exist some total order $<$ on $S$, but I'm not given this ordering and it could be anything. I am also given a collection of ...

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