[<< wikibooks] Suomen kieli ulkomaalaisille/Sisältö/us-uus-y-yys nominals
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Partitive formation varies for example 
lupaus (nom.) > lupauksen (gen.) lupausta (ptv.)

abstract noun lupaus permission is derived from luvata (to permit)
verb stem lupaa- + -us (abstract noun formation) > laupaus (with standard dropping of the extra vowel)kaipaus (nom.) > kaipauksen (gen.) kaipausta (ptv.)

abstract noun kaipaus longing or yearning is derived from kaivata (to yearnfor, long for, to miss)

verb stem kaipaa- +-us (abstract noun formation) > kaipaus (with standard dropping of the extra vowel)lisäys (nom.) > lisäystä (ptv.)

abstract noun lisäys addition or increase is derived from lisätä ('to increase. add to)
verb stem lisää- + -us (abstract nounn formation) > lisäys (with standard dropping of the extra vowel)lykkäys (nom.) > lykkäystä (ptv.)

abstract noun lykkäys postponement is derived from lykätä to postpone
stem lykkää- become (abstract noun, postponement)
The group that forms differently are usually formed from nouns and adjectives. These forms have genitive forms where the s transforms to d but partitive forms where the s transforms to t. 
vapaus (nom.) freedom > vapautta 
rakkaus becomes rakkautta
onnettomuus becomes onnettomuutta
ystävyys becomes ystävyyttä
kateus becomes kateuta
pimeys becomes pimeyttä
The rule is that if the word is derived from a nominal form, then the partitive will take the standard -ta or -tä ending which usually attached to nominals ending in a consonant. BUT, if the word is derived from an adjective (which may itself be derived from a verb) the s usually mutates to to a t before the -ta or -tä ending ius added.