Combinatorial reciprocity theorems

@article{Stanley1974CombinatorialRT,
  title={Combinatorial reciprocity theorems},
  author={Richard P. Stanley},
  journal={Advances in Mathematics},
  year={1974},
  volume={14},
  pages={194-253}
}
  • R. Stanley
  • Published 1 October 1974
  • Mathematics
  • Advances in Mathematics
A combinatorial reciprocity theorem is a result which establishes a kind of duality between two related enumeration problems. This rather vague concept will become clearer as more and more examples of such theorems are given. We shall be content in this paper with explaining the meaning of various reciprocity theorems via mere statements of results, together with clarifying examples. A rigorous treatment with detailed proofs appears in [11]. 
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