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UID:20250915T111935EDT-2369TVACw7@132.216.98.100
DTSTAMP:20250915T151935Z
DESCRIPTION:Markov number ordering conjectures.\n\nA Markov number is a num
 ber in the triple $(x\,y\,z)$ of positive integer solutions to the Diophan
 tine equation $x^2+y^2+z^2 = 3xyz$. Markov numbers are a classical topic i
 n number theory related to many areas of mathematics such as combinatorics
  and cluster algebras. Markov numbers are related to cluster algebras by M
 arkov snake graphs\, where a Markov snake graph is the snake graph of a cl
 uster variable of the once punctured torus. The number of perfect matching
 s of a Markov snake graph\, given by the numerator of the associated conti
 nued fraction\, is a Markov number. In this talk\, we discuss three conjec
 tures given in Martin Aigner’s book [A] that provide an ordering on the Ma
 rkov numbers $m_{p/q}$ for a fixed numerator $p$\, fixed denominator $q$ a
 nd a fixed sum $p+q$. [A] M. Aigner\, Markov's theorem and 100 years of th
 e uniqueness conjecture\, Springer 2010.\n
DTSTART:20171027T173000Z
DTEND:20171027T183000Z
LOCATION:Room PK-4323\, CA\, Seminar LACIM\, 201 Ave. President-Kennedy
SUMMARY:Michelle Rabideau\, University of Connecticut
URL:/mathstat/channels/event/michelle-rabideau-univers
 ity-connecticut-279855
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