images = {1, 2, 3, . . . }
images = {1, 2, 3, . . . , k}
(AP) : Addition Principle
(MP) : Multiplication Principle
(CP) : Complementation Principle
(IP) : Injection Principle
(BP) : Bijection Principle
(PP) : Pigeonhole Principle
(GPP) : Generalised Pigeonhole Principle
(PIE) : Principle of Inclusion and Exclusion
(GPIE) : Generalised Principle of Inclusion and Exclusion
(BT) : Binomial Theorem
LHS : Left-hand side
RHS : Right-hand side
|S| = the number of elements in the set S
img = the largest integer less than or equal to x
img = the largest integer less than or equal to x
FTA : Fundamental Theorem of Arithmetic
gcd : greatest common divisor
Bn = Bell number
= the number of ways of dividing n distinct objects into (nonempty) groups
C(n) = Catalannumber
= the number of shortest routes from O(0, 0) to A(n, n) which do not cross the diagonal y = x in the rectangular coordinate system
Dn = the number of derangements of images
s*(m, k) = the number of ways of arranging m distinct objects around k identical circles such that each circle has at least one object
s(m, k) = Stirling number of the first kind
= the coefficient of xk in the expansion
of x(x – 1)(x – 2) … (x – (m – 1))
S(m, k) = Stirling number of the second kind
= the number of ways of distributing m distinct objects into k identical boxes such that no box is empty
img = the number of r-element subsets of an n-element set
Pnr = the number of r-permutations of n distinct objects
AIME : American Invitational Mathematics Examination