Some genes can change their relative locations in a genome. Thus for different individuals of the same species, the orders of genes might be different. Such jumping genes are called transposons. A practical problem is to determine transposons in given gene sequences. Through an intuitive rule, we transform transposons from a biological concept into a rigorous mathematical object. Depending on whether the gene sequence is linear (each sequence has a fixed head and tail) or circular (we can choose any gene as the head, and the previous one is the tail), and whether genes have multiple copies, we classify the problem of determining transposons into four scenarios: (1) linear sequences without replicated genes; (2) circular sequences without replicated genes; (3) linear sequences with replicated genes; (4) circular sequences with replicated genes. With the help of graph theory, we design fast algorithms for different scenarios. We also derive some results that might be of theoretical interests in combinatorics.

翻译：一些基因可以在基因组中改变其相对位置。 因此,对于同一物种的不同个体来说,基因的顺序可能不同。 这种跳跃基因被称为转基因人。 一个实际的问题是确定特定基因序列中的转基因人。 通过直观规则,我们将转基因人从生物概念转变为严格的数学对象。取决于基因序列是线性的(每个序列都有固定头部和尾部)还是圆形的(我们可以选择任何基因作为头部,而前一个序列是尾部),以及基因是否有多个副本,我们把确定转基因的问题分为四种情况:(1) 没有复制基因的线性序列;(2) 没有复制基因的圆形序列;(3) 复制基因的线性序列;(4) 复制基因的圆形序列;(4) 复制基因的圆形序列。在图形理论的帮助下,我们设计了不同情景的快速算法。我们还得出一些结果,这些结果可能符合复写法的理论利益。