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SUMMARY:Brian Hopkins (Saint Peter's University)
DTSTART:20250523T183000Z
DTEND:20250523T185500Z
DTSTAMP:20260423T041654Z
UID:CANT2025/52
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/52/
 ">Scaled Arndt compositions</a>\nby Brian Hopkins (Saint Peter's Universit
 y) as part of Combinatorial and additive number theory (CANT 2025)\n\nLect
 ure held in CUNY Graduate Center - Science Center (4th floor).\n\nAbstract
 \nIn 2013\, Joerg Ardnt observed that integer compositions $c_1 + c_2 + \\
 cdots = n$ with $c_{2i-1} > c_{2i}$ for each positive $i$ are counted by t
 he Fibonacci numbers.  This was confirmed by the speaker and Tangboonduang
 jit in 2022 and we explored generalizations of this pair-wise condition in
 cluding $c_{2i-1} > c_{2i} + k$ for an affine parameter $k$.  In the curre
 nt work\, a collaboration with Augustine Munagi\, we consider scaling para
 meters\, integers $s$ and $t$\, and resolve some cases of the general cond
 ition $sc_{2i-1} > tc_{2i} + k$.  Techniques include generating functions 
 and combinatorial proofs.\n
LOCATION:https://researchseminars.org/talk/CANT2025/52/
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