Here are the commands to select dates based on the Mayan calendar:
To understand these commands, you need to understand the Mayan calendars. The long count is a counting of days with these units:
1 kin = 1 day 1 uinal = 20 kin 1 tun = 18 uinal 1 katun = 20 tun 1 baktun = 20 katun
Thus, the long count date 18.104.22.168.6 means 12 baktun, 16 katun, 11 tun, 16 uinal, and 6 kin. The Emacs calendar can handle Mayan long count dates as early as 22.214.171.124.3, but no earlier. When you use the g m l command, type the Mayan long count date with the baktun, katun, tun, uinal, and kin separated by periods.
The Mayan tzolkin calendar is a cycle of 260 days formed by a pair of independent cycles of 13 and 20 days. Since this cycle repeats endlessly, Emacs provides commands to move backward and forward to the previous or next point in the cycle. Type g m p t to go to the previous tzolkin date; Emacs asks you for a tzolkin date and moves point to the previous occurrence of that date. Similarly, type g m n t to go to the next occurrence of a tzolkin date.
The Mayan haab calendar is a cycle of 365 days arranged as 18 months of 20 days each, followed by a 5-day monthless period. Like the tzolkin cycle, this cycle repeats endlessly, and there are commands to move backward and forward to the previous or next point in the cycle. Type g m p h to go to the previous haab date; Emacs asks you for a haab date and moves point to the previous occurrence of that date. Similarly, type g m n h to go to the next occurrence of a haab date.
The Maya also used the combination of the tzolkin date and the haab date. This combination is a cycle of about 52 years called a calendar round. If you type g m p c, Emacs asks you for both a haab and a tzolkin date and then moves point to the previous occurrence of that combination. Use g m n c to move point to the next occurrence of a combination. These commands signal an error if the haab/tzolkin date combination you have typed is impossible.
Emacs uses strict completion (see Completion Exit) whenever it asks you to type a Mayan name, so you don't have to worry about spelling.