Transactions of the Mathematical Society
American Mathematical Society
We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite posets under the equivalence relation generated by converting minimal elements into maximal elements, or sources into sinks. We derive toric analogues for several features of ordinary partial orders, such as chains, antichains, transitivity, Hasse diagrams, linear extensions, and total orders.
Please use the publisher's recommended citation. http://www.ams.org/journals/tran/2016-368-04/S0002-9947-2015-06356-9/home.html