Ordered chains (such as chains of amino acids) are ubiquitous in biological cells, and these chains perform specific functions contingent on the sequence of their components. Using the existence and general properties of such sequences as a theoretical motivation, we study the statistical physics of systems whose state space is defined by the possible permutations of an ordered list, i.e., the symmetric group, and whose energy is a function of how certain permutations deviate from some chosen… Expand

It is argued that there is no distinct permutation glass phase for the simplest model considered here and how to extend the analysis to more complex Hamiltonians capable of novel phase behavior and replica symmetry breaking is discussed.Expand

Abstract This article traces the development and study of phase transitions from late last century to the present day. We begin with a brief historical sketch and a description of the statistical… Expand

Whatever you have to do with a structure-endowed entity Σ try to determine its group of automorphisms. .. You can expect to gain a deep insight into the constitution of Σ in this way. 1 Automorphism… Expand

Permutations and combinations binomial coefficients and multinomial coefficients the Pigeonhole principle and Ramsey numbers the principle of inclusion and exclusion generating functions recurrence… Expand