https://nova.newcastle.edu.au/vital/access/manager/Index ${session.getAttribute("locale")} 5 https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:28734 Wed 11 Apr 2018 12:10:08 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:26737 n/2 be the ratio of D(n) to the Hadamard upper bound. Using the probabilistic method, we prove new lower bounds on D(n) and R(n) in terms of d = n - h, where h is the order of a Hadamard matrix and h is maximal subject to h ≤ n. For example, [forumal cannot be replicated]. By a recent result of Livinskyi, d²/h^1/2 → 0 as n → 8, so the second bound is close to (πe/2)^-d/2 for large n. Previous lower bounds tended to zero as n → ∞ with d fixed, except in the cases d ∈ {0, 1}. For d ≥ 2, our bounds are better for all sufficiently large n. If the Hadamard conjecture is true, then d ≤ 3, so the first bound above shows that R(n) is bounded below by a positive constant (πe/2)^-3/2 > 0.1133.]]> Wed 11 Apr 2018 10:30:42 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:24113 [n]\A there is an A ∈ A with X ⊆ A or A ⊆ X, and (3) A is r-regular, i.e., every point x ∈ [n] is contained in exactly r members of A. We prove lower bounds on r, and we describe constructions for regular maximal antichains with small regularity.]]> Thu 30 May 2019 19:13:22 AEST ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:7412 Sat 24 Mar 2018 08:42:44 AEDT ]]> https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:21311 Sat 24 Mar 2018 07:54:39 AEDT ]]>