We prove several cases of the following theorem: Every free group word which is not a proper power can represent every permutation of an infinite set. The remaining cases will be proved in a ...

This is a preview. Log in through your library . Abstract In this article the concept of classifying space of a group is generalized to a classifying space of an arbitrary permutation representation.

Get ready to use the BigInteger data type as Dr. James McCaffrey of Microsoft Research demonstrates zero-based mathematical permutations with C#. A zero-based mathematical permutation of order n is a ...

A new proof from the Australian science fiction writer Greg Egan and a 2011 proof anonymously posted online are now being hailed as significant advances on a puzzle mathematicians have been studying ...

Representation theory was initially dismissed. Today, it’s central to much of mathematics. When representation theory emerged in the late 19th century, many mathematicians questioned its worth. In ...

Quantum spin systems occupy a central role in understanding magnetic phenomena and phase transitions at the microscopic level. In these systems, intrinsic angular momentum (spin) interactions give ...

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