[Avodah] prayers on YK and shabbat

[Eli Turkel]

What is the reason that ashkenazim dont say Avinu Malkenu on YK that is shabbat.
Much of the davening consists of requests. Evident examples are
"Shma Kolenu" and also the "Avinu Malkenu" right after "Modim" which in fact
has many similarities to the AM we say at the end.

Also why do some kehillot  do not say the 13 midot when YK coincides
with shabbat
(it was a discussion in the shul where I davened and they left it out).
We say it both at maariv and Neilah

-- 
Eli Turkel