六一 and short date format
This form of abbreviation is only reserved for special dates. Some popular Chinese holidays take this abbreviated form:


六一 == 儿童节
十一 == 国庆节
五一 == 劳动节


Any date can potentially become "special" following a major event or incident that occurred on that date or for a short period of time surrounding the said date. The abbreviated form is, therefore, used to identify the event:


四一二讲话 the speech made on April 12th or the April 12th speech


This is predicated on the fact that the listener is fully aware of both the date and the event in question. The abbreviated form would be meaningless otherwise.

A dot, "·", may be added between the month and the day in writing, especially when there is a possible ambiguity:


一·二四 January 24th
一二·四 December 4th


The reading stays the same, however.