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emiliocba gravatar image

Elements in the lattice An

Sorry in advance if this is not the right place to ask this simple question.

As it is usual, An=(a1,,an+1)Zn+1:a1++an+1=0. Now we define the norm (a1,,an+1):=i:ai>0ai. I would like an algorithm with input (n,k), that returns all elements in An with norm equal to k.

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Elements in the lattice An

Sorry in advance if this is not the right place to ask this simple question.

As it is usual, An=(a1,,an+1)Zn+1:a1++an+1=0. Now we define the norm (a1,,an+1):=i:ai>0ai. I would like an algorithm with input (n,k), that returns all elements in An with norm equal to k.

For example, if n=1 then (k,k) and (k,k) are all the elements in A1 with norm equal to k.

For n=2 and k=2, we have (2,0,2),(2,1,1),(2,2,0),(1,1,2),(1,2,1),(0,2,2),(0,2,2),(1,2,1),(1,1,2),(2,2,0),(2,0,2).