Toric partial orders

Develin, Mike; Macauley, Matthew; Reiner, Victor

doi:10.1090/tran/6356

Toric partial orders
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by Mike Develin, Matthew Macauley and Victor Reiner PDF

Trans. Amer. Math. Soc. 368 (2016), 2263-2287 Request permission

Abstract:

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.

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