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Answer on Other Math Question for Brandon Spatz

Question #2752
Let a set A = {a1, a2, ..., an}, where a1 < a2 < a3 < ... < an. Let A:k:n be as such; To present the idea, let n =4. so A:1:4 = a1 + a2 + a3 + a4, A:2:4 = (a1)(a2) + (a1)(a3) + (a1)(a4) + (a2)(a3) + (a2)(a4) + (a3)(a4), A:3:4 = (a1)(a2)(a3) + (a1)(a2)(a4) + (a1)(a3)(a4) + (a2)(a3)(a4) and A:4:4 = (a1)(a2)(a3)(a4). So if A = {1,2,3,4,5}, A:1:5 = 15, A:2:5 = 2+3+4+5+6+8+10+12+15+20, and so on. Keep in mind that since for example in A:3:n, (ai)(am)(an), where i,m,n are all natural numbers less than or equal to n, uses the same terms from A, we do not reuse them as (am)(ai)(ak) or any other variation of those 3 numbers. My question is, is there a symbol that refers to this, if so what is it, and what math area does this most directly fall under so I can further research it. Thank you
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