2014/07/12 by Roberto B. Corcino, Corcino, Roberto B., Ken Joffaniel M. Gonzales +3
Mathematics · #05A15 #11B65 #11B73 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15 #msc:11B65 #msc:11B73
paper · pdf · doi:10.48550/arxiv.1407.3343
New section on q-Bell numbers added, extended to case $s\in\mathbb R$
openalex publication_date 2014/07/12 · arxiv created 2014/08/20 · arxiv updated 2014/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The normal ordering coefficients of strings consisting of V,U which satisfy UV=qVU+hVs (s∈\mathbb N) are considered. These coefficients are studied in two contexts: first, as a multiple of a sequence satisfying a generalized recurrence, and second, as q-analogues of rook numbers under the row creation rule introduced by Goldman and Haglund. A number of properties are derived, including recurrences, expressions involving other q-analogues and explicit formulas. We also give a Dobinsky-type formula for the associated Bell numbers and the corresponding extension of Spivey's Bell number formula. The coefficients, viewed as rook numbers, are extended to the case s∈\mathbb R via a modified rook model.