Counting linear extension majority cycles in partially ordered sets on up to 13 elements

It is well known that the linear extension majority relation of a partially ordered set (P,≤P)(P,≤P) can contain cycles when at least 9 elements are present in PP. Computer experiments have uncovered all posets with 9 elements containing such cycles and limited frequency estimates for linear extension majority cycles (or LEM cycles) in posets on up to 12 elements are available. In this contribution, we present an efficient approach which allows us to count and store all posets containing LEM cycles on up to 13 elements.