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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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