Geodesic
Two approaches to normal order coefficients
Journal of integer sequences, Tome 20 (2017) no. 3.

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Summary: We consider the normal ordering coefficients of strings consisting of the symbols $V, U$ which satisfy the commutation rule $UV - qVU = hV^{s}$. 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.
Classification : 05A15, 11B65, 11B73
Keywords: Stirling number, normal ordering, rook theory, Bell number, symmetric function 
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     author = {Celeste, Richell O. and Corcino, Roberto B. and Gonzales, Ken Joffaniel M.},
     title = {Two approaches to normal order coefficients},
     journal = {Journal of integer sequences},
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     number = {3},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_3_a2/}
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Celeste, Richell O.; Corcino, Roberto B.; Gonzales, Ken Joffaniel M. Two approaches to normal order coefficients. Journal of integer sequences, Tome 20 (2017) no. 3. http://geodesic.mathdoc.fr/item/JIS_2017__20_3_a2/