The dimension of the Cartesian product of posets
C Lin - Discrete mathematics, 1991 - Elsevier
C Lin
Discrete mathematics, 1991•ElsevierWe give a characterization of nonforced pairs in the cartesian product of two posets, and
apply this to determine the dimension of P× Q, where P, Q are some subposets of 2 n and 2
m respectively. One of our results is dim S n 0× S m 0= n+ m− 2 for n, m⩾ 3. This generalizes
Trotter's result in [5], where he showed that dim S n 0× S n 0= 2n− 2. We also disprove the
following conjecture [2]: If P, Q are two posets and 0, 1∈ P, then dim P× Q⩾ dim P+ dim Q−
1.
apply this to determine the dimension of P× Q, where P, Q are some subposets of 2 n and 2
m respectively. One of our results is dim S n 0× S m 0= n+ m− 2 for n, m⩾ 3. This generalizes
Trotter's result in [5], where he showed that dim S n 0× S n 0= 2n− 2. We also disprove the
following conjecture [2]: If P, Q are two posets and 0, 1∈ P, then dim P× Q⩾ dim P+ dim Q−
1.
We give a characterization of nonforced pairs in the cartesian product of two posets, and apply this to determine the dimension of P× Q, where P, Q are some subposets of 2 n and 2 m respectively. One of our results is dim S n 0× S m 0= n+ m− 2 for n, m⩾ 3. This generalizes Trotter's result in [5], where he showed that dim S n 0× S n 0= 2n− 2. We also disprove the following conjecture [2]: If P, Q are two posets and 0, 1∈ P, then dim P× Q⩾ dim P+ dim Q− 1.
Elsevier
Showing the best result for this search. See all results