134 articles
Rank of a partition
The rank of a partition is a statistic introduced by Freeman Dyson in 1944, defined as the largest part minus the number of parts, explaining Ramanujan's congruences.
Repunit
A repunit is a whole number whose decimal digits are all 1, such as 11 or 111, with the name coined by Albert H. Beiler in 1966.
Significance of numbers in Judaism
The significance of numbers in Judaism covers symbolic numbers like seven, twelve, and 40, plus gematria, which gives Hebrew letters numerical values, making 18 the value of chai, or life.
Solid partition
A solid partition is a three-dimensional array of non-negative integers that never increases along any coordinate direction, visualized as unit cubes stacked in a corner of a room; counting them is unsolved.
Square number
A square number, or perfect square, is an integer that is the product of an integer with itself, such as 0, 1, 4, 9, 16, and 25.
Srinivasa Ramanujan (ஸ்ரீனிவாஸ் ராமானுஜன்)
Srinivasa Ramanujan Aiyangar (ஸ்ரீனிவாஸ் ராமானுஜன்) was an Indian mathematician, born 1887 and died 1920, known for work on partitions, infinite series, and his collaboration with G. H. Hardy at Cambridge.
Superior highly composite number
A superior highly composite number is an integer that maximizes the divisor-count ratio d(n)/n^ε for some ε, introduced by Srinivasa Ramanujan in his 1915 memoir on highly composite numbers.
Tetractys (τετρακτύς)
The tetractys (τετρακτύς, Tetraktys) is a triangular figure of ten points in four rows of one, two, three, and four, revered by the Pythagoreans and sworn upon in their oaths.
Triangular number
A triangular number counts objects arranged in an equilateral triangle, equaling the sum 1 + 2 + ... + n; the first few are 0, 1, 3, 6, and 10.
Triangular numbers
A triangular number is the sum of the integers from 1 to n, equal to n(n+1)/2; the sequence begins 0, 1, 3, 6, 10, 15, 21.
Tribonacci numbers
The Tribonacci numbers are an integer sequence in which each term is the sum of the three preceding terms, generalizing the Fibonacci numbers; they begin 0, 1, 1, 2, 4, 7.
Vampire number
A vampire number is a composite number whose digits can be split into two factors using the same digits, like 1260 = 21 × 60, named by Clifford Pickover in 1994.
Wheat and chessboard problem
The wheat and chessboard problem, also called the rice and chessboard problem, is a mathematical exercise where grains double on each square, totaling 18 quintillion grains across 64 squares.
Zero to the power of zero
Zero to the power of zero, written 0⁰, is the expression with both base and exponent zero, defined as 1 in combinatorics and computing standards but indeterminate in real analysis.