Patkós, Balázs (2019) On colorings of the Boolean lattice avoiding a rainbow copy of a poset. DISCRETE APPLIED MATHEMATICS, Availa. ISSN 0166-218X
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Abstract
Let F(n,k) (f(n,k)) denote the maximum possible size of the smallest color class in a (partial) k-coloring of the Boolean lattice Bn that does not admit a rainbow antichain of size k. The value of F(n,3) and f(n,2) has been recently determined exactly. We prove that for any fixed k if n is large enough, then F(n,k),f(n,k)=2(1∕2+o(1))n holds. We also introduce the general functions for any poset P and integer c≥|P|: let F(n,c,P) (f(n,c,P)) denote the maximum possible size of the smallest color class in a (partial) c-coloring of the Boolean lattice Bn that does not admit a rainbow copy of P. We consider the first instances of this general problem. © 2019
| Item Type: | Article |
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| Additional Information: | Export Date: 22 October 2019 CODEN: DAMAD Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFI, SNN 129364, K 116769 Funding text 1: Research was supported by the National Research, Development and Innovation Office — NKFIH, Hungary under the grants K 116769 and SNN 129364 . |
| Uncontrolled Keywords: | Forbidden subposet problems; Rainbow Ramsey problems; Set families; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 22 Oct 2019 13:42 |
| Last Modified: | 20 Apr 2023 09:12 |
| URI: | http://real.mtak.hu/id/eprint/102572 |
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