Exact antichain saturation numbers via a generalisation of a result of Lehman-Ron
EUROCOMB’23
120–126
Martin Aigner. Lexicographic matching in Boolean algebras. Journal of Combinatorial Theory, Series B, 14:187-194, 1973.
https://doi.org/10.1016/0095-8956(73)90001-4
Irina Ðanković and Maria-Romina Ivan. Saturation for small antichains. ArXiv preprint arXiv:2205.07392, 2022.
https://doi.org/10.37236/11262
Béla Bajnok and Shahriar Shahriari. Long symmetric chains in the boolean lattice. Journal of Combinatorial Theory, Series A, 75(1):44-54, 1996.
https://doi.org/10.1006/jcta.1996.0062
Paul Bastide, Carla Groenland, Hugo Jacob, and Tom Johnston. Exact antichain saturation numbers via a generalisation of a result of Lehman-Ron. https://arxiv.org/abs/2207.07391.
Robert P. Dilworth. A decomposition theorem for partially ordered sets. Annals of Mathematics, pages 161-166, 1950.
https://doi.org/10.2307/1969503
Dwight Duffus, David Howard, and Imre Leader. The width of downsets. European Journal of Combinatorics, 79:46-59, 2019.
https://doi.org/10.1016/j.ejc.2018.11.005
Michael Ferrara, Bill Kay, Lucas Kramer, Ryan R Martin, Benjamin Reiniger, Heather C Smith, and Eric Sullivan. The saturation number of induced subposets of the Boolean lattice. Discrete Mathematics, 340(10):2479-2487, 2017.
https://doi.org/10.1016/j.disc.2017.06.010
Dániel Gerbner, Balázs Keszegh, Nathan Lemons, Cory Palmer, Dömötör Pálvölgyi, and Balázs Patkós. Saturating Sperner families. Graphs and Combinatorics, 29(5):1355-1364, 2013.
https://doi.org/10.1007/s00373-012-1195-6
Curtis Greene and Daniel J. Kleitman. Strong versions of Sperner's theorem. Journal of Combinatorial Theory, Series A, 20(1):80-88, 1976.
https://doi.org/10.1016/0097-3165(76)90079-0
Jerrold R. Griggs. Collections of subsets with the Sperner property. Transactions of the American Mathematical Society, 269(2):575-591, 1982.
https://doi.org/10.1090/S0002-9947-1982-0637711-2
Maria-Romina Ivan. Saturation for the butterfly poset. Mathematika, 66:806-817, 2020.
https://doi.org/10.1112/mtk.12044
Maria-Romina Ivan. Minimal diamond-saturated families. Contemporary Mathematics, 3(2), 2022.
Balázs Keszegh, Nathan Lemons, Ryan R. Martin, Dömötör Pálvölgyi, and Balázs Patkós. Induced and non-induced poset saturation problems. Journal of Combinatorial Theory, Series A, 184:105497, 2021.
https://doi.org/10.1016/j.jcta.2021.105497
D. J. Kleitman. On an extremal property of antichains in partial orders. the lym property and some of its implications and applications. In M. Hall and J. H. van Lint, editors, Combinatorics, pages 277-290. Springer Netherlands, 1975.
https://doi.org/10.1007/978-94-010-1826-5_14
Eric Lehman and Dana Ron. On disjoint chains of subsets. Journal of Combinatorial Theory, Series A, 94(2):399-404, 2001.
https://doi.org/10.1006/jcta.2000.3148
Mark J. Logan. Sperner theory in a difference of boolean lattices. Discrete Mathematics, 257:501-512, 2002.
https://doi.org/10.1016/S0012-365X(02)00509-5
Ryan R Martin, Heather C Smith, and Shanise Walker. Improved bounds for induced poset saturation. The Electronic Journal of Combinatorics, 27(2):P2.31, 2020.
https://doi.org/10.37236/8949
Karl Menger. Zur allgemeinen kurventheorie. Fundamenta Mathematicae, 10(1):96-115, 1927.
https://doi.org/10.4064/fm-10-1-96-115
Natasha Morrison, Jonathan A. Noel, and Alex Scott. On saturated k-Sperner systems. The Electronic Journal of Combinatorics, 21(3):P3.22, 2014.
https://doi.org/10.37236/4136
Michael Saks. A short proof of the existence of k-saturated partitions of partially ordered sets. Advances in Mathematics, 33:207-2011, 1979.
https://doi.org/10.1016/0001-8708(79)90010-0
Emanuel Sperner. Ein Satz über Untermengen einer endlichen Menge. Mathematische Zeitschrift, 27(1):544-548, 1928.
https://doi.org/10.1007/BF01171114
Benny Sudakov, István Tomon, and Adam Zsolt Wagner. Uniform chain decompositions and applications. Random Structures & Algorithms, 60(2):261-286, 2022.
https://doi.org/10.1002/rsa.21034
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright © 2023 Paul Bastide, Carla Groenland, Hugo Jacob, Tom Johnston