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Equation 14 · Part 1 · The Hardest Unsolved Problems in AI Agent Architecture

Symbol n

(n2)=n(n−1)2,\binom{n}{2} = \frac{n(n-1)}{2},
nn

What this part means

the number of agents.

Its job in the formula

n occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Where the article explains it

For n agents that each need a channel to every other agent, the number of pairwise links a fully connected coordination topology requires is (n2)=n(n−1)2\binom{n}{2} = \frac{n(n-1)}{2}.

The passage around this formula

For n agents that each need a channel to every other agent, the number of pairwise links a fully connected coordination topology requires is (n2)=n(n−1)2\binom{n}{2} = \frac{n(n-1)}{2}. which grows quadratically in n even before accounting for the content sent over each link. That is a modeling assumption, not a law of nature…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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