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DC Field | Value | Language |
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dc.contributor.author | Borg, Peter | - |
dc.date.accessioned | 2021-05-17T07:09:41Z | - |
dc.date.available | 2021-05-17T07:09:41Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Borg, P. (2016). Intersecting integer partitions. The Australasian Journal of Combinatorics, 66(2), 265-275. | en_GB |
dc.identifier.uri | https://www.um.edu.mt/library/oar/handle/123456789/75639 | - |
dc.description.abstract | If a1, a2, . . . , ak and n are positive integers such that n = a1+a2+· · ·+ak, then the sum a1 + a2 + · · · + ak is said to be a partition of n of length k, and a1, a2, . . . , ak are said to be the parts of the partition. Two partitions that differ only in the order of their parts are considered to be the same partition. Let Pn be the set of partitions of n, and let Pn,k be the set of partitions of n of length k. We say that two partitions t-intersect if they have at least t common parts (not necessarily distinct). We call a set A of partitions t-intersecting if every two partitions in A t-intersect. For a set A of partitions, let A(t) be the set of partitions in A that have at least t parts equal to 1. We conjecture that for n ≥ t, Pn(t) is a largest t-intersecting subset of Pn. We show that for k > t, Pn,k(t) is a largest t-intersecting subset of Pn,k if n ≤ 2k − t + 1 or n ≥ 3tk5. We also demonstrate that for every t ≥ 1, there exist n and k such that t < k < n and Pn,k(t) is not a largest t-intersecting subset of Pn,k. | en_GB |
dc.language.iso | en | en_GB |
dc.publisher | Centre for Discrete Mathematics & Computing | en_GB |
dc.rights | info:eu-repo/semantics/openAccess | en_GB |
dc.subject | Mathematics | en_GB |
dc.subject | Logic, Symbolic and mathematical | en_GB |
dc.subject | Set theory | en_GB |
dc.subject | Hypergraphs | en_GB |
dc.title | Intersecting integer partitions | en_GB |
dc.type | article | en_GB |
dc.rights.holder | The copyright of this work belongs to the author(s)/publisher. The rights of this work are as defined by the appropriate Copyright Legislation or as modified by any successive legislation. Users may access this work and can make use of the information contained in accordance with the Copyright Legislation provided that the author must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the prior permission of the copyright holder. | en_GB |
dc.description.reviewed | peer-reviewed | en_GB |
dc.publication.title | The Australasian Journal of Combinatorics | en_GB |
Appears in Collections: | Scholarly Works - FacSciMat |
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File | Description | Size | Format | |
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Intersecting_integer_partitions_2016.pdf | 149.35 kB | Adobe PDF | View/Open |
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