A note on cycling LP examples with permutation structure

We study a particular class of cycling examples for the simplex algorithm which is characterized by a permutation structure, i.e. after a few iterations the simplex tableau is a column permutation of the initial tableau. Developing some matrix theory, among others, we formulate necessary and sufficient conditions, characterizing cycling examples with this structure and give some numerical examples. Hoffman's cycling example [Hoffman AJ. Cycling in the simplex algorithm. Report 2974, Washington DC: National Bureau of Standards; 1953] turns out to be a special member of this class. The answers on some related questions, studied very recently in Guerrero-García and Santos-Palomo [On Hoffman's celebrated cycling LP example. Computers & Operations Research, to appear] can be easily obtained in terms of the general framework.