You use yiyin when you are speaking to multiple people (or to one person formally). ye is for one person (informally).
If you are saying "eat together!", you're almost certainly talking to multiple people (one person can't really eat together with himself), so you need the plural form yiyin.
isha, it is not "yeyin" but "yiyin" for the command mood. The verbs "yemek" and "demek" are two exceptions. Have a look at this website: https://elon.io/learn-turkish/lesson/the-imperative-forms-of-yemek-and-demek. Very clear explanations.
It was mentioned briefly in Tips and Notes: "To Be" (scroll down to "Be as a Command"). But if you blinked, you may have missed it ;-)
Add the ending -In to the verb stem, which follows 4-way vowel harmony (olmak comes out as “olun”). This same suffix gets added to all verbs to make formal commands.
They don't mention the buffer letter, but based on this sentence, it seems it's -y-! At risk of over-complicating, here is an outside link about Turkish Imperatives (Unfortunately, there is no specific mention of the buffer letter for 2nd person formal... But all signs still point to -y- based on their example "okuyun".)
Shouldn't it be "yeyin" instead of "yiyin"? At least this is what online-conjugators like Verbix return.
Yomalyn, i found that: https://www.duolingo.com/dictionary/Turkish/yiyin/d2085d3f2af3f88a83f4ae5276127409, where "yiyin" is translated by" "eat, eat!"
I disagree strongly with this translation. The command is address to us (myself and at least one other). The correct way to express this in English is, "Let's eat together!" The expression "eat together" would not include myself. One would rarely, if ever say "Eat together". The only circumstance I can think of is addressing your children or similar group and telling them to eat together (without you).
PolymerDan, i don't feel myself concerned by this order. I give myself the order to a group of people. If "let's eat together" it would be translated in Turksih by "beraber yiyelim" with the optative suffix. Did you read "Suggestion" TIPS? You'll find the explanation.
That would be 'birbiri'. But it takes different suffixes according to the person.
Dün caddede birbirimizle karşılaştık: We met each other on the street yesterday. (birbiri-miz[since the person is 'biz'])
Birbirlerinin yüzlerine baktılar: They looked at each other's faces. (birbir-leri[since the person is 'onlar'])
Siz birbirinizi seviyorsunuz: You love each other. (birbiri-niz[since the person is 'siz'])
Interestingly, 'Birbirinizi yiyin.' means something like 'Argue(in a tiring way) with each other.', 'Wrangle with each other.' figuratively.