Four is written as four dots, the largest number the dot notation carries before the bar takes over at five. Four has a wider significance in Maya thought that is independent of the day count: the world has four sides and four corners, the directional colours are four with a fifth at the centre, and the Year Bearers are four.
Those four Year Bearers are a consequence of arithmetic rather than of symbolism, since a 365-day year advances the day sign by five places and four signs spaced five apart exhaust the twenty. It is a fair example of how difficult it is to separate the structural from the symbolic in this material: the number four arrives in the calendar by division, and it arrives in the cosmology independently, and the tradition treats them as the same four.
Maya numerals are written with a dot for one and a bar for five, and the coefficient of a day is written in exactly that way in the inscriptions, set beside the day sign in its cartouche. The system is positional and includes a sign for zero, which is why the Long Count can be written as a string of places, but within the 260-day count no number above thirteen ever occurs and the notation stays simple.
The term Self-Existing, applied to this coefficient in contemporary popular sources, belongs to Jose Arguelles's Dreamspell system of 1987 rather than to Maya tradition, and the atlas records it as such wherever the two are likely to be confused.
Sources Maya Hieroglyphic Writing: An IntroductionJ. Eric S. Thompson with Dreamspell: The Journey of Timeship Earth 2013Jose Arguelles