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SUMMARY:Christoph Koutschan\, "Binomial Determinants for Tiling Problems Y
ield to the Holonomic Ansatz"
DTSTART;VALUE=DATE-TIME:20210702T083000Z
DTEND;VALUE=DATE-TIME:20210702T093000Z
DTSTAMP;VALUE=DATE-TIME:20230129T022700Z
UID:indico-event-6754@indico.math.cnrs.fr
DESCRIPTION:We present and prove closed form expressions for some families
of binomial determinants with signed Kronecker deltas that are located al
ong an arbitrary diagonal in the corresponding matrix. They count cyclical
ly symmetric rhombus tilings of hexagonal regions with triangular holes. W
e extend a previous systematic study of these families\, where the locatio
ns of the Kronecker deltas depended on an additional parameter\, to famili
es with negative Kronecker deltas. By adapting Zeilberger's holonomic ansa
tz to make it work for our problems\, we can take full advantage of comput
er algebra tools for symbolic summation. This\, together with the combinat
orial interpretation\, allows us to realize some new determinantal relatio
nships. From there\, we are able to resolve all remaining open conjectures
related to these determinants\, including one from 2005 due to Lascoux an
d Krattenthaler.\n\nThis is joint work with Hao Du\, Thotsaporn Thanatipan
onda\, Elaine Wong.\n\nhttps://indico.math.cnrs.fr/event/6754/
URL:https://indico.math.cnrs.fr/event/6754/
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