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Update fixed_length_paths.md #1468

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Edited a line. "... instead of the sum" to " ... of the sum".

@@ -63,7 +63,7 @@ Then the following formula computes each entry of $L_{k+1}$:
$$L_{k+1}[i][j] = \min_{p = 1 \ldots n} \left(L_k[i][p] + G[p][j]\right)$$

When looking closer at this formula, we can draw an analogy with the matrix multiplication:
in fact the matrix $L_k$ is multiplied by the matrix $G$, the only difference is that instead in the multiplication operation we take the minimum instead of the sum.
in fact the matrix $L_k$ is multiplied by the matrix $G$, the only difference is that instead in the multiplication operation we take the minimum of the sum.
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@adamant-pwn adamant-pwn Jun 9, 2025

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in fact the matrix $L_k$ is multiplied by the matrix $G$, the only difference is that instead in the multiplication operation we take the minimum of the sum.
in fact the matrix $L_k$ is multiplied by the matrix $G$, the only difference is that instead in the multiplication operation we take the minimum instead of the sum, and the sum instead of the multiplication as the inner operation.

I think they mean that matrix multiplication is on $(\min, +)$ semiring instead of $(+, \cdot)$.

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Got it. Thanks.
Yeah it was little bit confusing, so...

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