
List of Frequently Used Notation
• A(n, k)numberofn-permutations with k − 1 descents
• c(n, k)numberofn-permutations with k cycles
• d(p) number of descents of the permutation p
• i(p) number of inversions of the permutation p
• I
n
(q) number of involutions of length n avoiding the pattern q
• n! n(n − 1) ···1
•
n
k
n!
k!(n−k)!
• [n] {1, 2, ···,n}
• [n] q
n−1
+ q
n−2
+ ···+1
• [n]! [n][n − 1] ···[1]
•
n
k
[n]!
[k]![n−k]!
• (n)
m
n(n − 1) ···(n −m +1)
• p(n) number of partitions of the integer n
• S
n
set of all n-permutations
• S
n
(q)numberofn-permutations avoiding the pattern q
• S
n,r
(q)numberofn-permutations containing exactly r copies of q
• S(n, k) number of partitions ...