A $q$-Multisum Identity Arising from Finite Chain Ring Probabilities

Authors :: Dousse, Jehanne
Osburn, Robert
Combinatoire, théorie des nombres (CTN)
Institut Camille Jordan [Villeurbanne] (ICJ)
École Centrale de Lyon (ECL)
Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL)
Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon)
Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL)
Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)
Centre National de la Recherche Scientifique (CNRS)
Dousse, Jehanne
Source :: The Electronic Journal of Combinatorics. 29
Publication Year :: 2022
Publisher :: The Electronic Journal of Combinatorics, 2022.
Abstract: In this note, we prove a general identity between a $q$-multisum $B_N(q)$ and a sum of $N^2$ products of quotients of theta functions. The $q$-multisum $B_N(q)$ recently arose in the computation of a probability involving modules over finite chain rings.<br />Comment: 7 pages, to appear in the Electronic Journal of Combinatorics

Subjects :: Mathematics - Number Theory
Applied Mathematics
[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Theoretical Computer Science
[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
Computational Theory and Mathematics
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
FOS: Mathematics
Mathematics - Combinatorics
Discrete Mathematics and Combinatorics
Number Theory (math.NT)
Combinatorics (math.CO)
Geometry and Topology
16P10, 16P70, 33D15
[MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

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