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A fair coin is tossed an even 2n number of times. Let D=|H-T| be the absolute difference in the number of heads and tails obtained. Then the probability distribution is given ...

Let L denote the partition lattice of the set {1,2,...,n}. The maximum element of L is M={{1,2,...,n}} (1) and the minimum element is m={{1},{2},...,{n}}. (2) Let Z_n denote ...

The study of number fields by embedding them in a local field is called local class field theory. Information about an equation in a local field may give information about ...

The word modulus has several different meanings in mathematics with respect to complex numbers, congruences, elliptic integrals, quadratic invariants, sets, etc. The modulus ...

Consider the number of sequences that can be formed from permutations of a set of elements such that each partial sum is nonnegative. The number of sequences with nonnegative ...

A perfect partition is a partition of a number n whose elements uniquely generate any number 1, 2, ..., n. {1,1,...,1_()_(n)} is always a perfect partition of n, and every ...

A plaindrome is a number whose hexadecimal digits are in nondecreasing order. The first few are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, ...

A Poisson process is a process satisfying the following properties: 1. The numbers of changes in nonoverlapping intervals are independent for all intervals. 2. The ...

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9. The concept ...

Let theta be an irrational number, define S(theta)={c+dtheta:c,d in N}, and let c_n(theta)+thetad_n(theta) be the sequence obtained by arranging the elements of S(theta) in ...