Skip to Main Content
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
18 Combinatorics of Permutations, Second Edition
lattice paths with n edges, exactly k of which are vertical. (Note the shift in
parameters: |A(n, k)| = A(n, k + 1), but this will not cause any confusion.)
Let P(n) be the set of labeled northeastern lattice paths that have edges
a
1
,a
2
,...,a
n
and that corresponding positive integers e
1
,e
2
,...,e
n
as labels,
so that the following hold:
(i) the edge a
1
is horizontal and e
1
=1,
(ii) if the edges a
i
and a
i+1
are both vertical, or both horizontal, then
e
i
e
i+1
,
(iii) if a
i
and a
i+1
are perpendicular to each other, then e
i
+ e
i+1
i +1.
The starting point of a path in P(n) has no additional significance. Let
P(n, k) be the set of all lattice paths in P(n) which have k vertical edges, and
let P (n, k)=|P(n, k)|.
PROPOSITI ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Introduction to Combinatorics, 2nd Edition

Introduction to Combinatorics, 2nd Edition

Martin J. Erickson

Publisher Resources

ISBN: 9781439850527