Mount Cayley, a volcano in southwestern British Columbia, Canada
Cayley's formula follows from Kirchhoff's theorem as a special case, since every vector with 1 in one place, −1 in another place, and 0 elsewhere is an eigenvector of the Laplacian matrix of the complete graph, with the corresponding eigenvalue being n.
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It is a generalization of Cayley's formula which provides the number of spanning trees in a complete graph.
George Cayley | Arthur Cayley | Cayley's formula | Cayley | Cayley–Purser algorithm | Neville William Cayley | Mount Cayley | Hugh Cayley | Cayley table | Cayley graph | Andrew Cayley |
Contributors included Robert Bisset (1758/9–1805), John Bowles (1751–1819), Arthur Cayley (1776–1848), George Gleig, Samuel Henshall (1764/5–1807), James Hurdis, John Oxlee (1779–1854), Richard Penn (1733/4–1811), Richard Polwhele, John Skinner (1744–1816), William Stevens (1732–1807), and John Whitaker (1735–1808), though as items were frequently published anonymously attributions are often unclear.
Sarah Flannery won the European Young Scientist of the Year award for her presentation of the Cayley–Purser algorithm, which was based on work she performed with Baltimore researchers during a short internship with the company.
The Bethe lattice or Cayley tree, is the Cayley graph of the free group on n generators.
This had won her the Intel Student Award which included the opportunity to compete in the 1998 Intel International Science and Engineering Fair in the United States.
Klein proposed an idea that all these new geometries are just special cases of the projective geometry, as already developed by Poncelet, Möbius, Cayley and others.
He made significant contributions to number theory, and the mathematical foundations of matrix algebra which would later lead to important contributions by Cayley and others.
Before the 20th century, definitions of primality were inconsistent, and significant mathematicians such as Goldbach, Lambert, Legendre, Cayley, and Kronecker wrote that 1 was prime.
André Joyal used this fact to provide a bijective proof of Cayley's formula, that the number of undirected trees on n nodes is nn − 2, by finding a bijection between maximal directed pseudoforests and undirected trees with two distinguished nodes.