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There are certain rites common to all Hindus though they are not included in the forty samskaras. the ears of a child must be pierced ceremonially ( "karna -vedhanam" ). Initiating a child into the alphabet ("aksarabhyasa"). is another samskara.
Cremation is not included in the forty samskaras but, as already pointed out, it is also a sacrifice, the last one, antyesti, and performed to the chanting of mantras by the son or a close relative of the deceased.
An ahitagnin 's cremation must be performed with the sacred fires he had tended, that is by bringing together his grhyagni and tretagni. The four fires will consume his body and transport his soul to a sacred world. If a person has not worshipped the tretagni and kept only the aupasanagni, his cremation must be performed with that fire.
There is no cremation, of course, for a sannyasin.
Since cremation is regarded as the last sacrifice, it follows that it is a rite that belongs to all except the inwardly mature and enlightened who take to sannyasa. If sannyasa were compulsory for all there would be no dahana-kriya or cremation mentioned in the sastras.
For a general background, please see here