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I was referring to this paper related to permutohedral lattice.

It states that the permutohedral lattice

$$ A_{d^*}= \bigcup_{k=0}^{d}\{\vec{x}\in H_d\ |\ \vec{x}\text{ is a remainder-$k$ point}\} $$

Where we call $\vec{x} \in H_d$ a remainder-$k$ point for some $k \in \{0, \dots , d\}$ iff all coordinates are congruent to $k$ modulo $d+1$.

I didn't get what this remainder-$k$ point means or being congruent to $k$ module $d+1$ means. I am just a beginner. I didn't get how the permutohedral lattice equation came to be like that in the end. Any suggestions?

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    Although the linked article refers to Gaussian filtering of data, both the article and the question appear to me to be more suitable for the mathematics site. I might be wrong but I see a lot of mathematics here but I don't see statistical, data mining or data visualization as a major part of it. My recommendation would be to migrate it to Math.2012-09-07

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