The Reciprocity Method
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In previous chapters, we defined ring homomorphisms \(\varphi\) on the ring of symmetric functions in order to find generating functions for permutation statistics. Doing this requires an a priori insightful definition of what the function \(\varphi\) should be. This chapter introduces the reciprocity method, which provides a way to come up with such a function \(\varphi\).
KeywordsReciprocity Method Permutation Statistics Descent Pair Pattern-avoiding Permutations Generating Function Manipulations
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