Create a list of all functions given a set of arguments

Question

I'm trying to examine some patterns on the permutation of elements in finite element functions. I'd like to create a list of all functions (256 of them) on 4 elements.

For example

{{(a, b), (b, c), (c, c), (d, a)}, {(a, c), (b, d), (c, c), (d, a)}, ... }

In all the methods I have tried I keep getting non-functional elements, i.e. things like

{{(a, b), (a, c), (c, d), (d, a)}, ... }

Any suggestions as for an easy way to do this?

What method have you tried such that you're getting 'non-functional' elements? — 2012rcampion, Mar 25 '15 at 16:41
Your "code" is not Mathematica-compatible. Would you mind fixing the round brackets? — Jinxed, Mar 25 '15 at 16:41
Also, let me check that I understand you correctly: you're trying to generate all mappings from the set {a, b, c, d} onto itself? — 2012rcampion, Mar 25 '15 at 16:42
@2012rcampion yes, exactly: your answer below was exactly what I was looking for. — bmf, Mar 26 '15 at 01:45

score 1 · Accepted Answer · answered Mar 25 '15 at 16:46

1

Try this:

set = {a, b, c, d};
maps = Thread[set -> #] & /@ Tuples[set, {Length[set]}]

If you want all permutations (one-to-one mappings from set onto set) replace Tuples with Permutations[set].

answered Mar 25 '15 at 16:46

2012rcampion

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This is great. And indeed, I was not looking for just 1-1 mappings. Thanks so much. Much better than other options using nests of combinations etc. Thanks again. – bmf Mar 26 '15 at 01:46

Create a list of all functions given a set of arguments

1 Answers1