Permutation Interpretations
This demo visually and interactively explains the two main interpretations of permutations: values as ranks (reordering) and values as entries (mapping). Compare the two interpretations to see how the same permutation array can mean different things in ranking, statistics, and combinatorics. Use the controls to randomize or reset the permutation and explore the differences.
The Source Data
One permutation, two completely different meanings
Key Insight: This permutation
[3, 1, 5, 2, 4] contains 5 numbers, but the meaning completely changes based on the permutation interpretation shown to the right.CliftonStrengths IDs
1Strategic
2Learner
3Achiever
4Analytical
5Responsibility
Permutation Array Values
Are these Ranks or Entries?
[3,1,5,2,4]
pos1pos2pos3pos4pos5
This array will be interpreted differently in each view to the right.
Experiment with different permutations to see how interpretations change
The interpretations to the right demonstrate how dramatically the meaning changes with the same underlying data
Interpretation 1: Values as Ranks
Each value in the permutation represents the rank of the corresponding strength.
Think of this as "What rank does each strength have?"
Think of this as "What rank does each strength have?"
1Strategic
→
Rank:3
2Learner
→
Rank:1
3Achiever
→
Rank:5
4Analytical
→
Rank:2
5Responsibility
→
Rank:4
Use Cases:
- Ranking systems (sports, competitions)
- Statistical analysis (percentiles)
- Performance evaluations
- Priority sorting (numpy.argsort)
Interpretation 2: Values as Entries
Each value in the permutation represents the entry at that position.
Think of this as "Which strength occupies each position?"
Think of this as "Which strength occupies each position?"
1Position 1
→
Achiever3
2Position 2
→
Strategic1
3Position 3
→
Responsibility5
4Position 4
→
Learner2
5Position 5
→
Analytical4
Use Cases:
- Mathematical permutation groups
- Algorithm implementations
- Data reordering operations
- Combinatorial analysis