# Manipulating combinatorial structures

I'm reading Knuth et al's Concrete Mathematics, chapter 7 on generating functions. They motivate the discussion by solving a combinatorial problem: find $T_n$, the number of ways in which one can arrange dominoes in a $2\times n$ area. The solution uses dominoes as if they were variables, some kind of abstract algebra. Is that safe? Are there other ways in which one can play with structures and get some useful results?

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Yes, it’s safe. It’s a simplified version of working with combinatorial species. – Brian M. Scott Feb 2 '13 at 0:19
Algebraic notation is a notable thing. It handles all kind of abuse in stride. ;-) – vonbrand Feb 2 '13 at 0:34