Two easy duality theorems for product partial orders
L. E. Trotter, Douglas B. West · Discrete Applied Mathematics · 1987
Two duality theorems are proved about the direct product of two partial orders. First, the size of the largest unichain (a chain fixed in one coordinate) equals the smallest number of semian-tichains (collections of elements in which no pair are comparable if they agree in either coordinate) needed to cover the elements of the product order. With analogous definitions, the size of a largest uniantichain equals the size of a smallest semichain covering.