X-Nico

Kirchhoff's theorem

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.

Anti-Jacobin Review

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.

Baltimore Technologies

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.

Cayley

Mount Cayley, a volcano in southwestern British Columbia, Canada

Cayley graph

The Bethe lattice or Cayley tree, is the Cayley graph of the free group on n generators.

Cayley–Purser algorithm

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.

Dobinski's formula

The number on both sides of the formula has come to be called the nth Bell number B_n, after the later work of Eric Temple Bell.

Erlangen program

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.

Giambelli's formula

In mathematics, Giambelli's formula, named after Giovanni Giambelli, expresses Schubert classes in terms of special Schubert classes, or Schur functions in terms of complete symmetric functions.

Jacques Philippe Marie Binet

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.

Jensen's formula

which is the Poisson formula for the harmonic function $f(z)|$.

Parity of zero

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.

Pseudoforest

André Joyal used this fact to provide a bijective proof of Cayley's formula, that the number of undirected trees on n nodes is n^n − 2, by finding a bijection between maximal directed pseudoforests and undirected trees with two distinguished nodes.

Savitzky–Golay filter

The summations in the matrix J^TJ can be evaluated in closed form,

Serial offender hunting patterns

Criminologist D. Kim Rossmo created the “Rossmo Formula” to explain his ideas on serial offenders and geographic profiling to determine where criminals lived and why specific locations were chosen as places to commit crimes.

Sums of powers

Faulhaber's formula expresses $1^k\; +\; 2^k\; +\; 3^k\; +\; \backslash cdots\; +\; n^k$ as a polynomial in n.

see also