caa a22 4500 44535867X CHVBK 20180317142908.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00493-011-2639-y doi (NATIONALLICENCE)springer-10.1007/s00493-011-2639-y On the non-existence of pair covering designs with at least as many points as blocks [Elektronische Daten] [Darryn Bryant, Melinda Buchanan, Daniel Horsley, Barbara Maenhaut, Victor Scharaschkin] We establish new lower bounds on the pair covering number C λ (υ,k) for infinitely many values of υ, k and λ, including infinitely many values of υ and k for λ=1. Here, C λ (υ,k) denotes the minimum number of k-subsets of a υ-set of points such that each pair of points occurs in at least λ of the k-subsets. We use these results to prove simple numerical conditions which are both necessary and sufficient for the existence of (K k − e)-designs with more points than blocks. János Bolyai Mathematical Society and Springer Verlag, 2011 Bryant Darryn Department of Mathematics, The University of Queensland, 4072, Brisbane, QLD, Australia aut Buchanan Melinda Department of Mathematics, The University of Queensland, 4072, Brisbane, QLD, Australia aut Horsley Daniel School of Mathematical Sciences, Monash University, 3800, Melbourne, VIC, Australia aut Maenhaut Barbara Department of Mathematics, The University of Queensland, 4072, Brisbane, QLD, Australia aut Scharaschkin Victor Department of Mathematics, The University of Queensland, 4072, Brisbane, QLD, Australia aut Combinatorica Springer-Verlag 31/5(2011-11-01), 507-528 0209-9683 31:5<507 2011 31 493 https://doi.org/10.1007/s00493-011-2639-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00493-011-2639-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bryant Darryn Department of Mathematics, The University of Queensland, 4072, Brisbane, QLD, Australia aut NATIONALLICENCE 700 1- Buchanan Melinda Department of Mathematics, The University of Queensland, 4072, Brisbane, QLD, Australia aut NATIONALLICENCE 700 1- Horsley Daniel School of Mathematical Sciences, Monash University, 3800, Melbourne, VIC, Australia aut NATIONALLICENCE 700 1- Maenhaut Barbara Department of Mathematics, The University of Queensland, 4072, Brisbane, QLD, Australia aut NATIONALLICENCE 700 1- Scharaschkin Victor Department of Mathematics, The University of Queensland, 4072, Brisbane, QLD, Australia aut NATIONALLICENCE 773 0- Combinatorica Springer-Verlag 31/5(2011-11-01), 507-528 0209-9683 31:5<507 2011 31 493 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer