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DTSTART:20240310T070000
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URL:/combinatorics-and-optimization/events/algebraic-an
d-enumerative-combinatorics-seminar-leigh-foster
SUMMARY:Algebraic and enumerative combinatorics seminar-Leigh Foster
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:The squish map and the SL_2 double dimer mode
l\n\nSpeaker\n Leigh Foster\n\nAffiliation\n University of 蓝莓视频\n\nLoc
ation\n MC 5479\n\n聽ABSTRACT: A plane partition\, whose 3D Young diagram
is made of unit\ncubes\, can be approximated by a \"coarser鈥� plane parti
tion\, made of\ncubes of side length 2. Two such approximations can be obt
ained by\n\"rounding up鈥� or \"rounding down鈥� to the nearest cube. We r
elate\nthis coarsening (or downsampling) operation to Young's squish map\,
\nintroduced in earlier work. We exhibit a related measure-preserving\nmap
between the 2-periodic single dimer model on the honeycomb graph\,\nand a
particular instance of Kenyon's SL_2 double dimer model on a\ncoarser hon
eycomb graph. This allows us to apply existing computations\nfrom the 2-pe
riodic single dimer partition function to a portion of\nthe parameter spac
e of the the harder double dimer model. We also\nspecialize our map and ex
hibit new criterion for the signed-tilability\nof a closed region on the h
oneycomb graph.\n\nTHERE WILL BE A PRE-SEMINAR PRESENTING RELEVANT BACKGRO
UND AT THE\nBEGINNING GRADUATE LEVEL STARTING AT 1PM\,\n
DTSTAMP:20250922T000105Z
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