Shofar, Sukkah and Lulav: Is There a Connection Between Shofar and Sukkah v’Lulav?

The Rambam’s Mishneh Torah is divided into fourteen books according to subjects or classes of laws. For example, the laws of Shabbos and the annual holidays that fall in different seasons and times of the year are in Sefer Zemanim, the Book of Seasons. Each book is further divided into sections of halakhos. In the case of Sefer Zemanim, those sections are Hilkhos Shabbos, Hilkhos Eruvin, Hilkhos Hamez u-Mazah, Hilkhos Shofar Sukkah v'Lulav, etc.

Why did the Rambam combine the laws of Shofar, Sukkah and Lulav into one set of halakhos?
Shofar is a mitzvah on Rosh Hashanah and ostensibly has no connection to yetzias mitzrayim. Sukkah is connected to yetzias mitzrayim and the agricultural aspect of the shalosh regalim as the chag ha’asif, the harvest festival. Lulav is perfomed on Sukkos and hence fits with Sukkos. But what is the connection between Shofar, on one hand, and Sukkah and Lulav, on the other hand?

Discussions in my Sukkah came up with the following answers:

1. There is no connection, but, the Rambam preferred to group them together rather than leave them as singletons
2. They are connected by the fact that they are mitzvos aseh, positive commandments, that occur in Tishrei
3. There are eight chapters in Hilkhos Shofar, Sukkah and Lulav corresponding to the eight days of Sukkos when Shmini Atzeres is included. The Rambam discusses the simcha shel ahava component of Shmini Atzeres in the eighth chapter of Hilkhos Shofar, Sukkah and Lulav

Rav Dovid Cohen says the connection is the celebration of success on Sukkos with Lulav on being forgiven during the y’mei ha’din of Rosh Hashanah and Yom Kippur. This is based on the Midrash Tehilllim 17.

True Kavanah During Shofar Blowing

R. Levi Yitzchak of Berditchev was looking for a Ba’al Toke’ah for his Beis Medrash. Candidates came from all over for the honorable position.

R. Levi Yitzchak interviewed them and asked:
--What kavanos do you have when you blow shofar?

Each one tried to impress R. Levi Yitzchak with special kavanos from the Ari and other great mekubalim. R. Levi Yitzchak was not impressed to engage any of them.

One day he was approached by a shofar blower who said:
--Rebbe, I am a plain Jew with four daughters to marry off and I do not have dowry for them. When I blow the shofar I think:
--Master of the universe, I did Your will and kept your mitzvos. So, You also, make my will Your will: Help me find husbands for my daughters.

R. Levi Yitzchak was overjoyed with this answer and said:
--Your kavanos are true kavanos. You shall be my ba’al toke’ah.