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Inclusion–exclusion principle. In combinatorics, a branch of mathematics, 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. where A and B are two finite sets and | S | indicates the cardinality of a ...
Exchange interaction is the main physical effect responsible for ferromagnetism, and has no classical analogue. For bosons, the exchange symmetry makes them bunch together, and the exchange interaction takes the form of an effective attraction that causes identical particles to be found closer together, as in Bose–Einstein condensation.
In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used. The rule of sum, rule of product, and inclusion–exclusion principle are often used for enumerative purposes. Bijective proofs are utilized to demonstrate that two sets have the same number of elements.
We need to consider only the outer 3p 2 electrons, for which it can be shown (see term symbols) that the possible terms allowed by the Pauli exclusion principle are 1 D , 3 P , and 1 S. Hund's first rule now states that the ground state term is 3 P, which has S = 1. The superscript 3 is the value of the multiplicity = 2S + 1 = 3.
In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. [ 1 ] For example, the electron configuration of the neon atom is 1s2 2s2 2p6, meaning that the 1s, 2s, and 2p subshells are occupied by two, two, and six ...
The statement of the general Möbius inversion formula [for partially ordered sets] was first given independently by Weisner (1935) and Philip Hall (1936); both authors were motivated by group theory problems. Neither author seems to have been aware of the combinatorial implications of his work and neither developed the theory of Möbius functions.
In nuclear physics, atomic physics, and nuclear chemistry, the nuclear shell model utilizes the Pauli exclusion principle to model the structure of atomic nuclei in terms of energy levels. [ 1 ] The first shell model was proposed by Dmitri Ivanenko (together with E. Gapon) in 1932. The model was developed in 1949 following independent work by ...
Host–guest chemistry is a branch of supramolecular chemistry in which a host molecule binds a so-called guest molecule or ion. The two components of the complex interact by non-covalent forces, most commonly by hydrogen-bonding. Binding between host and guest can be highly selective, in which case the interaction is called molecular ...