The family Poaceae includes over 10,000 species, among which are the most economically important cereals: maize, sorghum, rice, wheat, rye, barley, and oat. These cereals are very important components of human and animal food. Although divergence of the members of this family occurred about 40 million years ago, comparative genome analyses demonstrated that gene orders among species of this fam...

To understand evolution, and to discover how different species are related, gene order analysis is a useful tool. Problems in this area can usually be formulated in a combinatorial language. We regard genomes as signed, circular permutations, and evolutionary operations like reversals (reversing the order of a segment of genes) and transpositions (moving a segment of genes) are easy to describe...