2. (Jordan) A transitive permutation group of degree n > 1 contains a derangement. In fact (Cameron and Cohen) the proportion of derangements in a transitive group G is at least 1/n. Equality holds if and only if G is sharply 2transitive, and hence is the affine group {x 7→ ax + b : a, b ∈ F, a 6= 0} over a nearfield F. The finite nearfields were determined by Zassenhaus. They all have prime po...

In this paper I draw the distinction between intuitive and theory-relative accounts of the time reversal symmetry and identify problems with each. I then propose an alternative to these two types of accounts that steers a middle course between them and minimizes each account’s problems. This new account of time reversal requires that, when dealing with sets of physical theories that satisfy cer...

Processes mediated by small nucleophilic catalysts are currently experiencing a renaissance. In addition to competing with well-established metal-catalyzed reactions, there is a tempting opportunity to invert conventional reactivity patterns by exploiting the concept of polarity reversal (umpolung). Following this strategy, aldehydes can be turned into acylanion equivalents through covalent act...

In this paper, we present two new results of layered permutation densities. The first one generalizes theorems from Hästö (2003) and Warren (2004) to compute the permutation packing of permutations whose layer sequence is (1, l1, l2, . . . , lk) with 2−a−1 ≥ k (and similar permutations). As a second result, we prove that the minimum density of monotone sequences of length k + 1 in an arbitraril...

An overview is given of the use of symmetry considerations for aperiodic crystals. Superspace groups were introduced in the seventies for the description of incommensurate modulated phases with one modulation vector. Later, these groups were also used for quasi-periodic crystals of arbitrary rank. Further extensions use time reversal and time translation operations on magnetic and electrodynami...

Three possibilities for the origin of CP violation are discussed: (1) the Standard Model in which all CP violation is due to one parameter in the CKM matrix, (2) the superweak model in which all CP violation is due to new physics and (3) the Standard Model plus new physics. A major goal of B physics is to distinguish these possibilities. CP violation implies time reversal violation (TRV) but di...