The suspension spectrum of a group can be thought of as a kind of group ring S[G]. It would be interesting to try to see how many of the classical results about Hopf-algebras (or just group rings) one could obtain for such objects.
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Can you say more?
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I was thinking about how positive integers are represented as combinations of other positive integers. There are additive and multiplicative partition functions. There's the integer complexity: https://en.wikipedia.org/wiki/Integer_complexity …
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