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Combinatorics of Permutations, 2nd Edition
book

Combinatorics of Permutations, 2nd Edition

by Miklos Bona
April 2016
Intermediate to advanced content levelIntermediate to advanced
478 pages
14h 44m
English
Chapman and Hall/CRC
Content preview from Combinatorics of Permutations, 2nd Edition
Permutations and the Rest. Algebraic Combinatorics of Permutations. 285
of a Standard Young Tableau Z if i appears in a row in Z that is strictly
above the row in which i + 1 appears in Z.
THEOREM 7.15
Let π S
n
,andleti [n 1].Theni is a descent of π if and only if i is a
descent of Q(π).
PROOF First let us assume that i D(p), that is, π
i
i+1
. We need
to show that the insertion of π
i+1
results in the addition of a new box to the
P -tableaux that is below the box resulting from the insertion of π
i
.
As π
i
i+1
, we know that π
i+1
gets inserted to the first row of P (π)
weakly on the left of π
i
. If the insertion of π
i
ended in the first row, then we
are ...
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Publisher Resources

ISBN: 9781439850527