CN saturated Partitions
نویسنده
چکیده
Stephan-Yl ~n Solomon Let L be a lan~'uage over m vocmb~Ja~y V ~nd let de~ot~. by E (V) the s,t of ml! enuSv~lence relmtlon~ (partitions) on V. If ~ ~ E (V) and x ~ V then we sb~ll denote by ~(v) the cell of ~ containing the elmment 7. Defini%ion I. A p~rtition ~GE(V) is s~id to be smturated ev~-VY i (I ~imn) there exlst such elements x~ Our purpose i.,~ to find (in the cese of m finite vocebu-I mry) th~ gre,~test smtnrmted p_-rtit~on Z of the Imn~.umme. Definition 2. Let~E(V) sod x, y~V. We shall s8y that x ~-domimatms y (x3~y) if for every string xI...x~E L wh~e xi= x there exist such ~lem~nts x~. We c~n ~wtroduce now the p~rtitlon ~* , cmlBed tb~ asterisk of the pertition ~ : 7~y If both 7 ~-~-~y ~nd yPx hold true. Theorem I, ~ is ~ smtt)rmt~d pmrtition if mnd only if is finer tbmn The connection between the ~sterisk ~nd the ~erivative of ~ pm~t~t~on is given by: In orQer that #'=~,~ it is necessary ~nd sufficient thmt 2 be saturated.
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