Tachanun is omitted from Shacharis, however in Selichos Tachanun is recited even if one is reciting Selichos after Alos. [By the Mincha prior to Erev Rosh Hashanah [28th of Elul] Tachanun is recited. Likewise in Kerias Shema Sheal Hamita of the night of Erev Rosh Hashanah Tachanun is recited.]
Keil Erech Apayim: Keil Erech Apayim is omitted from Davening on Erev R”H that falls on Monday.
 581/3; Siddur Admur
 The reason: As Tachanun is omitted on every Erev Yom Tov. [Tur; Levush 581 brought in Kaf Hachaim 581/72] To note that by other Holidays we stop saying Tachanun several days prior to the holiday: By Pesach from Rosh Chodesh Nissan; By Shavuos from the 1st of Sivan; By Sukkos from the 11th of Tishrei.
 M”A 581/13; Elya Raba 581/33; Levush 581
 Luach Kolel Chabad; See previous chapter on “Elul” Halacha 15J
 Admur in Siddur “However by the Mincha before Erev Rosh Hashanah..”; Levush 131/6; P”M 581 A”A 13; Kaf Hachaim 581/74; This is evident from the fact that the Poskim rule Selichos is said on that night.
 Hiskashrus 896 Just as Tachanun is recited by Selichos.
 Admur in Siddur based on Kneses Hagedola 131/3; Peri Chadash 131/1; Mamar Mordechai 131/6 that whenever Tachanun is omitted Lamnatzeiach is omitted; Divrei Nechemia 131/9; Kaf Hachaim 581/78 states that so is the custom of Sefaradim. Certainly then on Erev Rosh Hashanah, which is Erev Yom Tov, Lamnatzeaich is omitted.
Other Poskim: Some Poskim rule that Lamnatzeaich is recited on Erev Rosh Hashanah being it is a fast day. [Levush; Minhagim; M”E 581/49] See Admur 429/12 which rules like Rama 131/1 that Lamnatzeiach may be recited even on a day that Tachanun is omitted. However no reference is made to Erev Rosh Hashanah which is Erev Yom Tov.]
 Takana of Rebbe Rayatz, recorded in Siddur Tehillas Hashem prior to Musaf Davening of Shabbos.
 Siddur Tehillas Hashem [from 1978 and onwards with the Rebbe’s approval] based on Sichas Kodesh 6th Tishrei 1975 that the Rebbe equates Kel Erech Apayim with Lamnatzeiach. See Shulchan Menachem 3/293; Glosses of Rav Raskin p. 165; Hiskashrus 438 p. 17; To note however that the Rebbe himself did recite Kel Erech Apayim even when Tachanun was not recited. [Rav Raskin ibid]
Ruling of Admur: In the Shulchan Aruch [429/12; 602/4] Admur rules that Kel Erech Apayim is recited with exception to Erev Pesach. This follows the ruling of the Hagahos Maimanis. [Some explain that it is for this reason that Admur in 602/4 placed this ruling in parentheses, as it is not brought in previous Poskim in Shulchan Aruch. [Shulchan Menachem ibid footnote 2] Vetzaruch Iyun as it is brought by Admur in 429/12 without parentheses, and is likewise clearly implied from the Rama 429/2] To note that also in the Siddur before Kel Erech Apayim Admur lists a number of days that it is to be omitted on, thus implying it is not always omitted when Tachanun is not said.
Ruling and explanation of Divrei Nechemia: The Divrei Nechemia 131/9 brings three opinions regarding the saying of Keil Erech Apayim: 1) It is only omitted by a day that Halel is recited or a day that has the status of a Yom Tov like Erev Pesach. [This is the opinion of the Rama 429/2] 2) It is omitted on every Erev Yom Tov and on Isru Chag. 3) Every day that Tachanun is omitted so is Lamnatzeiach. [so rules Peri Chadash 131] The Divrei Nechemia concludes that regarding Lamnatzeiach we rule like the third opinion, however regarding Keil Erech Apayim we rule like the opinion that rules it is to be recited.
The reason behind the Rebbe’s ruling: The Rebbe explains that the ruling in the Shulchan Aruch of Admur follows the ruling of the Rama that differentiates between the laws of Tachanun and that of Lamnatzeiach. However according to Admur in the Siddur that rules Lamnatzeiach is always omitted when Tachanun is not said then likewise Kel Erech Apayim is to be omitted in all days that Tachanun is not said. [Sichas Kodesh ibid, printed in Shulchan Menachem ibid] As for the reason why Kel Erech Apayim is omitted this is because it mentions sin, and we do not desire to mention sin on any day that Tachanun is omitted. [See Shaar Hakolel 36/2; Shulchan Menachem ibid footnote 5]
 Siddur Admur
 The reason: The reason for this is because this Psalm represents supplications and is hence omitted by times of joy. [Shaar Hakolel 11/23 based on Seder Hayom]