Sorry, no online dictionaries contain the exact phrase poset height.
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Reverse dictionary results:
1. chain
 2. chaining
3. antigen
4. digraph
5. functional
6. graph
7. lagrangian
8. lattice
9. permutation
10. polyhedron
 11. ultrafilter
12. algorithm
13. algebra
14. automaton
15. axiomatization
16. graphs
17. lattices
18. module
19. nucleotide
20. parametrization
 21. polyhedra
22. quanta
23. rf
24. above
25. abreast
26. absolute ceiling
27. accordance
28. acme
29. aconcagua
30. acro-
 31. acrophobia
32. adams
33. adansonia
34. aerie
35. aloft
36. alp
37. alps
38. alt
39. alti-
40. altimeter

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You can look up the words in the phrase individually using these links:   poset ?   height ?
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pose*to search for words beginning with pose, or
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