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SUMMARY:Augustine O. Munagi (University of the Witwatersrand\, South Afric
 a)
DTSTART:20260718T190000Z
DTEND:20260718T192500Z
DTSTAMP:20260710T111525Z
UID:CANT2026/89
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/89/
 ">A Bessenrodt-Ono inspired inequality for compositions proved constructiv
 ely</a>\nby Augustine O. Munagi (University of the Witwatersrand\, South A
 frica) as part of Combinatorial and additive number theory seminar (CANT 2
 026)\n\nLecture held in Science Center in the CUNY Graduate Center (4th fl
 oor).\n\nAbstract\nIn 2016 Bessenrodt-Ono published an analytic proof of t
 he inequality $p(a+b)\\leq p(a)p(b)$\, where $p(n)$ is the partition funct
 ion and $a\,b$ are positive integers with $a+b>8$. In this talk we conside
 r a similar result for $c(n)$\, the number of integer compositions of $n$\
 , and show that $c(a+b)>c(a)c(b)$ for all positive integers $a\,b$. Beside
 s numerical verifications\, we provide a constructive bijective proof base
 d on the inherent symmetry of compositions. It is known that such a proof 
 is still elusive in the partitions case. We also give an application of ou
 r machinery to efficient generation of compositions.\n
LOCATION:https://researchseminars.org/talk/CANT2026/89/
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