Journal of Integer Sequences, Vol. 20 (2017), Article 17.3.5

Two Approaches to Normal Order Coefficients

Richell O. Celeste
Institute of Mathematics and Natural Sciences Research Institute
University of the Philippines - Diliman
Quezon City, Philippines 1101

Roberto B. Corcino
Mathematics Department
Cebu Normal University
Cebu City, Philippines 6000

Ken Joffaniel M. Gonzales
Department of Physical Sciences and Mathematics
University of the Philippines — Manila
Manila, Philippines 1004


We consider the normal ordering coefficients of strings consisting of the symbols V, U which satisfy the commutation rule UV - qVU = hVs. These coefficients are studied using two approaches. First, we continue the study by Varvak, where the coefficients were interpreted as q-rook numbers under the row creation rook model introduced by Goldman and Haglund. Second, we express the coefficients in terms of a kind of generalization of some symmetric functions. We derive identities involving the coefficients including some explicit formulas.

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(Concerned with sequences A001147 A001497 A004747 A007559 A008277 A008544 A035342 A035469 A039683 A051141 A051142 A122848 A132393 A203412 A265604 A265605 A265606 A271703.)

Received August 22 2016; revised versions received October 16 2016; January 3 2017. Published in Journal of Integer Sequences, January 14 2017.

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