Notation for unordered product of sets

Question

Frequently, when referring to the edges of an undirected graph $G=(V,E)$, I want to write that $E \subset V \times V$, which isn't correct since the Cartesian product is ordered and the edges are not.

This motivates my question: is there a common notation for a product of sets $A$ and $B$ defined by $\{ \{a,b\} ~|~ a \in A ,~ b \in B \}$?

$[X]^2$ is used to refer to the set of unordered pairs from a set $X$ (and $[X]^n$ for $n$-tuples). — universalset, Dec 05 '13 at 15:56
Per the modified Question, if $A$ and $B$ are disjoint, then the distinction between ordered and unordered pairs is without essential substance. Given an unordered pair, ${a,b}$ we can identify the corresponding ordered pair $(a,b)$ by virtue of $A\cap B = \emptyset$. — hardmath, Dec 05 '13 at 16:16
I'm not trying to put words in your mouth; you do not imply disjointness. I'm merely pointing out a reason that one often avoids the "messiness" of saying $C = { {a,b} \mid a \in A, b \in B }$. — hardmath, Dec 05 '13 at 16:31
(Sorry posted my answer first here as a comment...) Please delete this ... — InfinitelyInquisitive, Sep 14 '14 at 16:28
See also: https://math.stackexchange.com/questions/112935/notation-for-all-subsets-of-size-2 — Vincent Labatut, Nov 06 '17 at 09:54

score 6 · Accepted Answer · answered Sep 10 '14 at 13:58

6

I use $E \subseteq \binom{V}{2}$. Although, I have seen it used elsewhere, it's probably not a standard notation.

answered Sep 10 '14 at 13:58

ChargeShivers

1,737

This notation is often used in graph theory. – Frunobulax Sep 14 '14 at 16:57
This strikes me as awkward in general though because binomial coefficients generally mean "without replacement" – Sheridan Grant Jun 24 '19 at 02:57
@SheridanGrant $\binom{V}{2} = {X \subseteq V : |X| = 2}$. Is this not without replacement? – user76284 Oct 27 '19 at 20:29
@user76284 no recollection of this comment but I appear to be a doofus, you're right – Sheridan Grant Oct 28 '19 at 22:29

score 2 · Answer 2 · answered Sep 14 '14 at 16:29

2

We used $\bar{\times}$ (but without the gap between the bar and the times symbol) in the algebraic graph theory lectures I've attended some years ago. I liked it, however I don't know how common it is.

answered Sep 14 '14 at 16:29

InfinitelyInquisitive

329

1

FYI, it's not common at all (at least I've never seen it anywhere). Maybe in some fields, but certainly not in all of mathematics. – Najib Idrissi Sep 14 '14 at 17:18

Notation for unordered product of sets

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