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 Jun 9 accepted What is the established algebraic form for interleaving or zipping a pair of equal length sets? Jun 9 revised An expression to represent all possible arrangments of a set of length n into 3 (infintely sized) bins? deleted 11 characters in body Jun 9 comment What is the established algebraic form for interleaving or zipping a pair of equal length sets? @Travis, Henning, thanks - I do mean ordered sets, as per Travis' comment Jun 9 asked What is the established algebraic form for interleaving or zipping a pair of equal length sets? Jun 9 revised An expression to represent all possible arrangments of a set of length n into 3 (infintely sized) bins? added 542 characters in body Jun 9 revised An expression to represent all possible arrangments of a set of length n into 3 (infintely sized) bins? edited body Jun 8 comment An expression to represent all possible arrangments of a set of length n into 3 (infintely sized) bins? @ErickWong, Well put. Thanks. Jun 8 comment An expression to represent all possible arrangments of a set of length n into 3 (infintely sized) bins? Ahh... beginning to sink in! Thanks. Jun 8 comment An expression to represent all possible arrangments of a set of length n into 3 (infintely sized) bins? @ErickWong Probably down to my inexperience in this area, but, looking at this, I couldn't see how the duplicate empty sets would be included e.g. {1,2},{},{}}. Jun 8 awarded Commentator Jun 8 comment An expression to represent all possible arrangments of a set of length n into 3 (infintely sized) bins? yes perhaps I wrong to dismiss it. I would expect $3^n$ output sets as you suggest. However I couldn't see how the duplicate empty sets would be introduced, e.g. {{1,2},{},{}} Jun 8 revised An expression to represent all possible arrangments of a set of length n into 3 (infintely sized) bins? added 265 characters in body Jun 8 revised An expression to represent all possible arrangments of a set of length n into 3 (infintely sized) bins? added 7 characters in body Jun 8 comment An expression to represent all possible arrangments of a set of length n into 3 (infintely sized) bins? @string thanks. Whilst there are some similarities, I don't think it does exactly correspond. Jun 7 asked An expression to represent all possible arrangments of a set of length n into 3 (infintely sized) bins? Apr 22 comment How do I express, algebraically, this comparison of two sets of sets? I meant $|A1|+|A2|+|A3|$. But, yes, the sets are disjoint. Also, as there always be 3 subsets, I will probably choose to represent $J$ as $3$. Apr 22 accepted How do I express, algebraically, this comparison of two sets of sets? Apr 22 comment How do I express, algebraically, this comparison of two sets of sets? Thanks @goblin. I think I want $\sum_{j:J}|A_j|$ as the denominator. Is the ambiguity in my question related to the $+$ symbols in the denominators of the example? Apr 22 comment How do I express, algebraically, this comparison of two sets of sets? @GA316 I mean the combined length of $A_1$, $A_2$ and $A_3$ (=6). I'm not sure of the correct representation at the moment. Apr 22 revised How do I express, algebraically, this comparison of two sets of sets? deleted 6 characters in body