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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
202 Combinatorics of Permutations, Second Edition
for the vector space C[n]. In particular, P
i
(n) is a linear combination of
polynomials of the form (n + i)
j
. Therefore, using generating functions,
n0
P
i
(n)f(n + i)x
n
is a linear combination of generating functions of
the form
n0
(n + i)
j
f(n + i)x
n
(5.5)
with complex coefficients.
Compare formulae (5.4) and (5.5). We see that the left-hand side of
(5.5) almost agrees with x
ji
u
(j)
, that is, they can only differ in finitely
many terms with all negative coefficients. Let the sum of these terms
be R
i
(x) x
1
K[x
1
], a Laurent-polynomial. If we multiply (5.1) by
x
n
and sum over all non-negative n,weget
0=
#
i
a
ij
x
j
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Publisher Resources

ISBN: 9781439850527