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The p orbital can hold a maximum of six electrons, hence there are six columns in the p-block. Elements in column 13, the first column of the p-block, have one p-orbital electron. Elements in column 14, the second column of the p-block, have two p-orbital electrons. The trend continues this way until column 18, which has six p-orbital electrons.
The upper p-series is formed by taking π 2i−1 = p′ and π 2i = p; there is also a lower p-series. A finite group is said to be p-nilpotent if and only if it is equal to its own p′,p-core. A finite group is said to be p-soluble if and only if it is equal to some term of its upper p-series; its p-length is the length of its upper p-series.
[1] A split graph may have more than one partition into a clique and an independent set; for instance, the path a–b–c is a split graph, the vertices of which can be partitioned in three different ways: the clique {a, b} and the independent set {c} the clique {b, c} and the independent set {a} the clique {b} and the independent set {a, c}
A partially balanced incomplete block design with n associate classes (PBIBD(n)) is a block design based on a v-set X with b blocks each of size k and with each element appearing in r blocks, such that there is an association scheme with n classes defined on X where, if elements x and y are ith associates, 1 ≤ i ≤ n, then they are together ...
The generator, or lead vector, p b of the chain is a generalized eigenvector such that (A − λI) b p b = 0. The vector p 1 = (A − λI) b−1 p b is an ordinary eigenvector corresponding to λ. In general, p i is a preimage of p i−1 under A − λI. So the lead vector generates the chain via multiplication by A − λI.
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In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.