MATHEMATICAL proofs, GROUP theory, MATHEMATICAL analysis, ALGORITHMS, MATHEMATICAL models
Abstract
We give an elementary, nongroup theoretic proof that exactly half of the 15! arrangements of the fifteen puzzle can be restored to the natural order. [ABSTRACT FROM AUTHOR]
MATHEMATICAL models, BIOTIC communities, SPECIES distribution, ALGORITHMS, MARKOV processes
Abstract
The article discusses the concept of checkerboard distributions and species combinations in ecological communities. Topics include the assembly rules by ecologist Jared Diamond, the randomization and incorporation of algorithms in determining species combinations, and the use of a Markov chain approach.