A framework for the description of a number of members of the AUTOMATH family

A framework for the description of a number of members of the AUTOMATH family by N.G. de Bruijn 1. Introduction. I

Sorting arrays by means of swaps

AbstractAs a preparation to the study of a particular sorting machine, the sorting of arrays by sequences of swaps is treated in this paper. In particular it is shown that if a sequence of “miniswaps” sorts the worst possible arrangement of an array, then it sorts every arrangement of that array. The case of permutation arrays was treated before by R.W. Floyd

Penrose patterns are almost entirely determined by two points

AbstractIt is shown that for any Penrose pattern π and for any positive number ε we can find two vertices P and Q of π such that in any large circular disk all but a fraction of at most ε of the vertices is common to all Penrose patterns (with the same pieces, in the same directions) that have P and Q as vertices