It is prohibited to fast immediately after the holiday of Shavuot. Rem"a: And we do not say Tachanun from the beginning of Rosh Chodesh Sivan until the 8th day, which is after the post-holiday day (Hagahot Maimoni, Hil' Tefillah Umnagim). We have the custom to spread out plants on Shavuot in the synagogue and in houses, as a memory for the happiness of the receiving of the Torah. We have a custom everywhere to eat dairy food on the first day of Shavuot. And it seems to me that the reason is: It is like the two foods that are taken on the evening of Pesach, a reminder of the Korban Pesach and a reminder of the Korban Chagiga, so too we eat a dairy food followed by a meat food, and we bring with them two loaves on the table in place of the Mizbeach, and thus there will be a reminder of the two loaves that were brought on "The day of the Bikkurim."
In remembrance of the joy of receiving the Torah: for there were grasses around Mount Sinai, as it says "The flocks and cattle shall not graze..." Latter sages wrote that in places where it is the custom to give out fragrant grasses in the synagogue, they should not give them out from Barukh SheAmar until after the Amida, so that one may bless over them (the blessing for fragrant vegetation)-- because during that period it is forbidden to interrupt (the prayer). There is a custom to stand trees in the synagogues and homes in remembrance that on Shavuot judgment takes place for the fruits of the tree. The Gr"a abolished this custom because now it is the ritual of the (non-Jewish) nations to put up trees on their holiday.
At four set times the world is judged: On Pesah in respect to the produce. On Shavuot in respect to the fruit of the tree. On Rosh Hashanah all the people of the world pass before Him like a division of soldier [a numerus], as it says, “He who fashions the hearts of them all, who discerns all their doings” (Psalms 33:15). And on Sukkot they are judged in respect of rain.