We can construct an occupation representation of Slater determinants by the odometer method. Consider \( N_{sp} = 12 \) and \( N=4 \). Start with the first 4 states occupied, that is:

• \( sd(1,:)= 1,2,3,4 \) (also written as \( |1,2,3,4 \rangle \))

Now increase the last occupancy recursively:

• \( sd(2,:)= 1,2,3,5 \)
• \( sd(3,:)= 1,2,3,6 \)
• \( sd(4,:)= 1,2,3,7 \)
• \( \ldots \)
• \( sd(9,:)= 1,2,3,12 \)

Then start over with

• \( sd(10,:)= 1,2,4,5 \)

and again increase the rightmost digit

• \( sd(11,:)= 1,2,4,6 \)
• \( sd(12,:)= 1,2,4,7 \)
• \( \ldots \)
• \( sd(17,:)= 1,2,4,12 \)