Vibration theory of olfaction have a vibrational energy mode compatible with the difference in energies between two energy levels on the receptor, so electrons can travel through the molecule via inelastic electron tunneling, triggering the signal transduction pathway. The vibration theory is discussed in a popular but controversial book by Chandler Burr. The odor character is encoded in the ratio of activities of receptors tuned to different vibration frequencies, in the same way that color is encoded in the ratio of activities of cone cell receptors tuned to different frequencies of light. An important difference, though, is that the odorant has to be able
Parity of a permutation of formula_1 into disjoint cycles, which can be composed in any order because they commute. A cycle formula_49 involving formula_50 points can always be obtained by composing formula_51 transpositions (2-cycles): so call formula_51 the "size" of the cycle, and observe that, under this definition, transpositions are cycles of size 1. From a decomposition into formula_54 disjoint cycles we can obtain a decomposition of formula_1 into formula_56 transpositions, where formula_57 is the size of the th cycle. The number formula_58 is called the discriminant of formula_1, and can also be computed as if we take care to include the fixed points