We give a formula for the number of convex sets in a product of two finite totally ordered sets with the product order and discuss related counting problems.
Brandy Barnette. Warren Nichols. Tom Richmond. "The number of convex sets in a product of totally ordered sets." Rocky Mountain J. Math. 49 (2) 369 - 385, 2019. https://doi.org/10.1216/RMJ-2019-49-2-369