MATH Seminar
| Title: Maximal Chains and Antichains in Finite Partially Ordered Sets |
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| Seminar: Combinatorics |
| Speaker: Dwight Duffus of Emory University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2009-10-16 at 4:00PM |
| Venue: W306 |
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| Abstract: Fix integers n and k with n at least k, and n, k > 2. With Bill Sands, we proved that if P is a finite partially ordered set and every maximal chain C of P has between n and n + (n - k)/k - 2) elements, then P must contain k pairwise disjoint maximal antichains. We also constructed a family of examples to show that these inequalities are tight. We raised and made observations about the dual problem, which Dave Howard and Tom Trotter [Georgia Tech] have recently solved. |
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