High order congruences for M-ary partitions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489823" target="_blank" >RIV/00216208:11320/24:10489823 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=CHfF~4V.dn" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=CHfF~4V.dn</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10998-024-00579-0" target="_blank" >10.1007/s10998-024-00579-0</a>

Result language
angličtina
Original language name
High order congruences for M-ary partitions
Original language description
or a sequence M = (m i )ooi=0 of integers such that m0 = 1, m i >= 2 for i >= 1, let p M (n)denote the number of partitions of n into parts of the form m0m1 . . . m r . In this paper weshow that for every positive integer n the following congruence is true:p M (m1m2 . . . m r n - 1) IDENTICAL TO 0(modrN-ARY PRODUCTt=2M(m t , t - 1)),where M(m, r) := mgcd(m,lcm(1,...,r)) . Our result answers a conjecture posed by Folsom,Homma, Ryu and Tong, and is a generalisation of the congruence relations for m-ary partitionsfound by Andrews, Gupta, and Rodseth and Sellers.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GM21-00420M" target="_blank" >GM21-00420M: Universal Quadratic Forms and Class Numbers</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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