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In combinatorial mathematics, the Bell numbers count the possible partitions of a set. These numbers have been studied by mathematicians since the 19th century, and their roots go back to medieval Japan. In an example of Stigler's law of eponymy, they are named after Eric Temple Bell, who wrote about them in the 1930s.
The figure shows the 13 weak orderings on three elements. Starting from , the ordered Bell numbers are. 1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, 102247563, ... (sequence A000670 in the OEIS). When the elements to be ordered are unlabeled (only the number of elements in each tied set matters, not their identities) what remains is a ...
The periodic table, also known as the periodic table of the elements, is an ordered arrangement of the chemical elements into rows (" periods ") and columns (" groups "). It is an icon of chemistry and is widely used in physics and other sciences. It is a depiction of the periodic law, which states that when the elements are arranged in order ...
Bell series. In mathematics, the Bell series is a formal power series used to study properties of arithmetical functions. Bell series were introduced and developed by Eric Temple Bell. Given an arithmetic function and a prime , define the formal power series , called the Bell series of modulo as: {\displaystyle f_ {p} (x)=\sum _ {n=0}^ {\infty ...
Thus, the number of monomials that appear in the partial Bell polynomial is equal to the number of ways the integer n can be expressed as a summation of k positive integers. This is the same as the integer partition of n into k parts. For instance, in the above examples, the integer 3 can be partitioned into two parts as 2+1 only.
Time-keeping on this clock uses arithmetic modulo 12. Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed ...
In mathematics, the Bernoulli polynomials, named after Jacob Bernoulli, combine the Bernoulli numbers and binomial coefficients. They are used for series expansion of functions, and with the Euler–MacLaurin formula. These polynomials occur in the study of many special functions and, in particular, the Riemann zeta function and the Hurwitz ...
Periodic table (electron configurations) Configurations of elements 109 and above are not available. Predictions from reliable sources have been used for these elements. Grayed out electron numbers indicate subshells filled to their maximum. Bracketed noble gas symbols on the left represent inner configurations that are the same in each period.
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