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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
48 Combinatorics of Permutations, Second Edition
where P (n, k) is the probability that at the end of the trials there are k
empty boxes. Then it can be proved that
B
r
(n)=S(n, n r, l)
(n r)!
n!
l
by showing that both sides satisfy the same recurrence relations. Then,
by the formula P (k, n)=
n
r=k
(1)
rk
r
k
B
r
(n), our claim follows.
4. The volume of R
n,k
is equal to A(n, k)/k!. A nice combinatorial proof
was given by Richard Stanley [241]; though the result was probably
known by Laplace. The main element of Stanley’s proof is the following
measure-preserving map. It is straightforward that A(n, k)/k!isthe
volume of the set S
n,k
of all points (x
1
,x
2
,
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Publisher Resources

ISBN: 9781439850527