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= | {1, 2, 3, . . . } |
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= | {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 |
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= | the largest integer less than or equal to x |
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= | 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 ![]() |
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)) |
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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 | |
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= | 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 |