Ordered sets with small width and large jump number
Tóm tắt
The following result is proved in this note: For any positive integers w and t, if an ordered set P has jump number at least (t+1)
w−1, then either the width of P is more than w, or P has a tower, i.e., a linear sum of pairs of noncomparable elements, of height more than t.
Tài liệu tham khảo
M. Chein and M. Habib (1982) Jump number of dags and partial orders with Dilworth number 2, preprint.