Sorry, no online dictionaries contain the exact phrase alternating permutations.
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Reverse dictionary results:
1. touch
2. oscillograph
3. allele
4. allelomorph
5. allomorph
6. alternatives
7. choices
8. flywheel
9. other
10. otherwise
11. pinwheel
12. substitute
13. substitutes
14. substitution
15. terry
16. alternation
17. change
18. changing
19. checker
20. checkered
21. direct
22. motor
23. phase
24. rectifier
25. rhythm
26. stagger
27. steps
28. var
29. alternation of generations
30. bond
31. conjugation
32. cycle
33. diode
34. lead
35. ondograph
36. rectification
37. staggered
38. staggering
39. transformation
40. warble

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You can look up the words in the phrase individually using these links:   alternating ?   permutations ?
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alte*to search for words beginning with alte, or
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