Combinatorial Number System

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I recently read up Combinatorial Number System. I wanted to know how would we find the nth combination when arranged in lexicographic manner and when "repetition was allowed". Eg: {1,2,3} the 6th combination is {1,3} ({1},{2},{3},{1,1},{1,2},{1,3})

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What you're describing here is like a basis of numeration in $n+1$ with each number containing at least one $0$ missing.