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CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:Claire Levaillant\, USC\n\nAbstract : An Egyptian fraction is a
decomposition of a rational into a sum of distinct unit fractions. These f
ractions appear in some of the oldest mathematical manuscripts in Egypt in
1650 BC and regained interest with ErdÃ¶s in the mid 50's. Fibonacci in 1202
was the first to provide a greedy algorithm in order to obtain such decomp
osition for any choice of rational number.\nWhile several other general alg
orithms grew over the years to attempt to minimize the length and largest i
nteger of the decomposition\, no general algorithms were ever provided to g
enerate all the decompositions of a given length.\n In this talk\, we focus
on the decomposition of the unit and offer a general algorithm to find all
the decompositions of a given length involving only primes 2 and q as fact
ors in the denominators\, with q any set odd prime and imposing that the ex
ponents of 2 are less than or equal to 2. We also provide a general algorit
hm for counting these solutions for a given length of the decomposition.
DTEND:20231030T200000Z
DTSTAMP:20240910T184841Z
DTSTART:20231030T190000Z
GEO:34.022409;-118.291027
LOCATION:Kaprielian Hall (KAP)\, 414
SEQUENCE:0
SUMMARY:Combinatorics Seminar: Egyptian fraction decompositions of the unit
of given length with denominators 2^a.q^b with q set odd prime and a<3
UID:tag:localist.com\,2008:EventInstance_44642391849898
URL:https://calendar.usc.edu/event/combinatorics_seminar_egyptian_fraction_
decompositions_of_the_unit_of_given_length_with_denominators_2aqb_with_q_se
t_odd_prime_and_a3
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