Order Theory/Series-parallel order

parallel order Let be a family of ordered sets, and define . Then the parallel order on is defined to be the order . parallel composition Let be a family of ordered sets, and define . Then the pair , where is the parallel order on , is called the parallel composition of the sets . series order Let be a preordered set, and let be a family of ordered sets over . The series order on induced by is the order on given by . series composition Let be a preordered set, and let be a family of ordered sets, and define . Then the pair , where is the series order on , is called the series composition of the sets over . series-parallel order A series-parallel order is the order of an ordered set that arises from a family of singleton ordered sets (the order being the order that turns into a poset) by applying parallel composition and series composition over a finite number of times.