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SUMMARY:Manjil P. Saikia (Ahmedabad University\, Ahmedabad\, India)
DTSTART:20260717T193000Z
DTEND:20260717T195500Z
DTSTAMP:20260710T111638Z
UID:CANT2026/72
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/72/
 ">Hook length biases in t-regular and t-core partitions</a>\nby Manjil P. 
 Saikia (Ahmedabad University\, Ahmedabad\, India) as part of Combinatorial
  and additive number theory seminar (CANT 2026)\n\nLecture held in Science
  Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nRecently\, t
 he theory of hook length biases has emerged as a prominent research topic.
  Led by Ballantine\, Burson\, Craig\, Folsom\, and Wen\, hook length biase
 s are being explored for ordinary partitions\, odd versus distinct partiti
 ons\, self-conjugate versus distinct odd partitions. Recently\, Singh and 
 Barman opened the door to hook length biases in $t$-regular partitions as 
 well. \n\nThe objective of this talk is two fold. First\, we present a pre
 viously unobserved connection of hook-lengths in $t$-regular partitions wi
 th certain distinct parts partitions. Second\, we extend the theory of hoo
 k length biases to $t$-core partitions. For example\, let $a_{t\,k}(n)$ de
 note the number of hooks of length $k$ in all $t$-core partitions of $n$\,
  then we find that $a_{3\,1}(n) \\ge a_{3\,2}(n) \\ge a_{3\,4}(n)$ and $a_
 {4\,1}(n) \\ge a_{4\,3}(n)$ for all $n$. Most of the methods employed in t
 his work are combinatorial. Joint work with Talukdar\; and Baruah\, Das\, 
 and Mahanta.\n
LOCATION:https://researchseminars.org/talk/CANT2026/72/
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