Thirteen is written as two bars and three dots, and it closes a trecena. The following day carries the number one again with the next sign in the twenty, so the transition from thirteen to one is where the two cycles visibly reset against each other.
Thirteen has a wider place in Maya thought. Colonial Yucatec sources name a group of thirteen deities, the Oxlahun Ti Ku, against the nine of the underworld; thirteen levels are commonly given for the upper world in Postclassic Mesoamerican cosmology; the Short Count of the Postclassic period runs thirteen katuns; and the Long Count origin is written 13.0.0.0.0, with a completed thirteen baktuns behind it. The number recurs at every scale of the system.
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.
Cosmic, the name given to this coefficient in modern popular literature, comes from Jose Arguelles's Dreamspell of 1987 and is not a Maya term. What is Maya is the number thirteen itself and the structural role it plays, which is considerable and needs no addition.
Sources Maya Hieroglyphic Writing: An IntroductionJ. Eric S. Thompson with Dreamspell: The Journey of Timeship Earth 2013Jose Arguelles