We characterise the class of all claw-free t-perfect graphs by forbidden t-minors. Moreover, we show that claw-free t-perfect graphs are 3-colourable. Such a colouring can be obtained in polynomial time.

A graph is called t-perfect, if its stable set polytope is defined by nonnegativity, edge and odd-cycle inequalities. We characterise the class of all claw-free t-perfect graphs by forbidden t-minors. Moreover, we show that claw-free t-perfect graphs are 3-colourable. Such a colouring can be obtained in polynomial time.

Take a centered random walk Sn and consider the sequence of its partial sums An := ∑n i=1 Si. Suppose S1 is in the domain of normal attraction of an α-stable law with 1 < α ≤ 2. Assuming that S1 is either right-exponential (that is P(S1 > x|S1 > 0) = e−ax for some a > 0 and all x > 0) or right-continuous (skip free), we prove that P { A1 > 0, . . . , AN > 0 } ∼ CαN 1 2α− 1 2 as N → ∞, where Cα ...

We investigate Abelian primitive words, which are words that are not Abelian powers. We show the set of Abelian primitive words is not context-free. We can determine whether a word is Abelian primitive in linear time. Also different from classical primitive words, we find that a word may have more than one Abelian root. We also consider enumeration of Abelian primitive words.

We introduce a new number–theoretic spin chain and explore its thermodynamics and connections with number theory. The energy of each spin configuration is defined in a translation–invariant manner in terms of the Farey fractions, and is also expressed using Pauli matrices. We prove that the free energy exists and exhibits a unique phase transition at inverse temperature β = 2. The free energy i...