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Ong Hok Ham (1 May 1933 – 30 August 2007) [1] [2] [3] was an eminent Chinese Indonesian historian considered one of the leading experts on Indonesian history during the 19th century Dutch colonial rule. His particular area of knowledge centered on events in Java during the period, and he authored a number of works dealing with the subject.
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures.It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
For any pair of positive integers n and k, the number of k-tuples of non-negative integers whose sum is n is equal to the number of multisets of size k − 1 taken from a set of size n + 1, or equivalently, the number of multisets of size n taken from a set of size k, and is given by
3 out of 4638576 [1] or out of 580717, [2] if rotations and reflections are not counted as distinct, Hamiltonian cycles on a square grid graph 8х8. Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed.
Further difficulties include Ham's being referred to as "the youngest son", when all other lists make him Noah's second son. [12] Biblical scholar Nahum Sarna says that the biggest challenge of the narrative is why Canaan was cursed, rather than Ham, [ 12 ] and that the concealed details of the shameful incident bear the same reticence as ...
Venn diagram showing the union of sets A and B as everything not in white. In combinatorics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as
Ham [a] (in Hebrew: חָם), according to the Table of Nations in the Book of Genesis, was the second son of Noah [1] and the father of Cush, Mizraim, Phut and Canaan. [2] [3] Ham's descendants are interpreted by Josephus and others as having populated Africa. The Bible refers to Egypt as "the land of Ham" in Psalm 78:51; 105:23, 27; 106:22; 1 ...
One of the earliest uses of analytic techniques for an enumeration problem came from Srinivasa Ramanujan and G. H. Hardy's work on integer partitions, [4] [5] starting in 1918, first using a Tauberian theorem and later the circle method.