The senior undergraduates at my (mathematics) department have this impression that postgraduate programmes don't want to admit multiple applicants from the same university in the same application cycle. So they are coordinating so that no two people apply to the same programme (i.e. if one student applies to the University of X, the others make sure not to apply to the university of X).
Is this true? If a postgraduate PhD programme accepts a candidate from one university, will this doom the chances of other candidates applying from that same university in that application cycle?
I am primarily interested in answers from Math PhD programmes, but also would be interested in answers from other fields.