The general boson normal ordering problem

@article{Blasiak2003TheGB,
  title={The general boson normal ordering problem},
  author={Pawel Blasiak and Karol A. Penson and VI AllanI.SolomonUniversityofParis and France. and Polish Academy of Sciences and Krak{\'o}w and Poland and The Open University and Milton Keynes and UK.},
  journal={Physics Letters A},
  year={2003},
  volume={309},
  pages={198-205}
}
Abstract We solve the boson normal ordering problem for F[(a † ) r a s ] , with r , s positive integers, [a,a † ]=1 , i.e., we provide exact and explicit expressions for its normal form N {F[(a † ) r a s ]} , where in N (F) all a 's are to the right. The solution involves integer sequences of numbers which are generalizations of the conventional Bell and Stirling numbers whose values they assume for r = s =1. A comprehensive theory of such generalized combinatorial numbers is given including… Expand
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