The basic concept is that for any given person, no two romantic partners fulfil the same kind of needs.
Let us take all the possible ways in which a romantic partner (since we are talking about multiple partners for the same person, usuallly happening at different points of time in the person’s life, I don’t want to use the term “long-term gene propagating partner”) can help you out. The kind of needs that she can fulfil. Make a list of them, and represent them as a vector.
And to this, add a vector of binaries. Let us call it the “need vector”. You might have guessed that an element of this vector is 1 if the partner fulfils this particular need and 0 otherwise. So for each of your romantic partners (spanning across space and time), construct such a vector. Yeah of course some of these needs are more important than others so you might think you might want to give weights, but that is not the purpose of this exercise.
The Pauli Exclusion Principle in quantum mechanics states that no two electrons can have the same four quantum numbers. Similarly the P Polie Exclusion Principle in romantic relationships states that no two of your romantic partners have the same need vector. That the needs vector of any two of your romantic partners have a hamming distance of at least 1.
This principle has certain important consequences. Given that any two of your romantic partners are separated by a Hamming distance of at least 1 and using the Neha Natalya-xkcd argument, the number of romantic partners you can possibly have in your lifetime is bounded from above by 2^n, where n is the length of your need vector. So contrary to intuition, this shows that promiscuous people actually have a larger set of needs from romantic partners than committed people.
The only flaw in your theory is that you assume the “need vector” as being binary. The 2^n bound would actually be 2^kn where k>1.