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SUMMARY:Jeu de taquin
DTSTART;VALUE=DATE-TIME:20191118T093000Z
DTEND;VALUE=DATE-TIME:20191118T103000Z
DTSTAMP;VALUE=DATE-TIME:20201130T083550Z
UID:indico-event-5306@indico.math.cnrs.fr
DESCRIPTION:The Jeu de taquin\, also known as the 15-puzzle\, is a puzzle
introduced by Sam Loyd in the 1870s. The objective of the puzzle is to obt
ain the numbers 1 to 15 in the correct ordering\, by performing moves whic
h ’slide’ a neighboring number into the empty space. Considering the s
tarting position as a permutation in S 16 \, including the empty space as
the 16th element\, we show that the puzzle is solvable if and only if the
corresponding permutation restricts (in some sense) to an even permutation
in the alternating group A 15. We also present a graph theoretic generali
zation of the 15-puzzle. Finally we show how the idea behind the ’slidin
g moves’ in the 15-puzzle gives rise to an equivalence relation in the s
et of skew-symmetric standard Young tableaux. These are objects that play
an important role in algebraic combinatorics\, and especially find use in
the representation theory of Lie algebras and algebraic groups.\n\nhttps:/
/indico.math.cnrs.fr/event/5306/
LOCATION:ENS 435
URL:https://indico.math.cnrs.fr/event/5306/
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