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May one get a haircut during Shloshes Yimei Hagbala, and when Erev Shavuos coincides with Shabbos?
Even if it is past one’s accustomed mourning period, according to Kabbalah, one is to avoid getting a haircut throughout the period of Sefira, including during the Shloshes Yimei Hagbala, until Erev Shavuos, and so is the Chabad custom.
On Erev Shavuos: It is permitted, and is a Mitzvah, to get a haircut on Erev Shavuos. One may do so even past midday.
Erev Shavuos that falls on Shabbos: When Erev Shavuos coincides with Shabbos, one may get a haircut on Erev Shabbos which is the 48th day of the Omer. This applies even according to the Kabbalistic ruling and Chabad custom. [One may begin to take a haircut after sunrise of Erev Shabbos, although not the night before.] However, when Shavuos falls on Monday, one is not to get a haircut on Erev Shabbos, but only on Erev Shavuos.
 Custom of Arizal, brought in Peri Eitz Chaim 22:7; Shaar Hakavanos 86; Nehar Shalom 25; Igeres Ramaz 2; Birkeiy Yosef 493:6; Moreh Baetzba 8:221; Minchas Elazar 4:44; Kaf Hachaim 493:13
Other opinions: Some write that according to even according to Kabbalah one may get a haircut on the 48th day of Omer and that so was the custom of Rav Chaim Vital. [Minchas Elazar ibid]
 Hayom Yom p. 53; Sefer Haminhagim p. 86 [English] “The Rebbe Rashab was uneasy with those which took haircuts during the Shloshes Yimei Hagbala”
 Moreh Baetzba 8:221; Minchas Elazar 3:65; Kaf Hachaim 493:13; Shevach Hamoadim p. 235 footnote 10 in name of Rav Shmuel Levitin that so was the custom in Lubavitch; Otzer Minhagei Chabad p. 290
Other opinions: The Rashash questioned whether one may get a haircut on the 48th day of Omer even in such a case. He concluded that if he would not have been forced into it, he would not have gotten a haircut on the 48th. [Nehar Shalom p. 25]
 The reason: Although in general, based on the custom of the Arizal, we avoid haircuts until Erev Shavuos, this only applies when Erev Shavuos falls on a weekday, as one cannot enter into the festival with improper attire. Furthermore, it is recorded in Shaar Hakavanos that Rav Chaim Vital was always accustomed to get a haircut on the 48th day of Omer. Some learn this itself was due to Kabalistic reasons. Furthermore, even according to the Rashash who leaned to be stringent not to take a haircut on Erev Shabbos in such a coincidence, nevertheless he too forced himself to do so. Hence there is no room to be stringent on the above, and on the contrary one should do so. [See Minchas Elazar ibid]
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 Hagahos Chasam Sofer 493