Steiner Triple Systems With High Discrepancy
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Wiley Open Access
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| Format: | Artículo Open Access |
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2025
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| author | Lior Gishboliner Stefan Glock Amedeo Sgueglia |
| author_facet | Lior Gishboliner Stefan Glock Amedeo Sgueglia Lior Gishboliner Stefan Glock Amedeo Sgueglia |
| collection | Wiley Open Access |
| contents | Steiner Triple Systems With High Discrepancy Lior Gishboliner Stefan Glock Amedeo Sgueglia Journal of Combinatorial Designs ABSTRACT In this paper, we initiate the study of discrepancy questions for combinatorial designs. Specifically, we show that, for every fixed and , any ‐colouring of the triples on admits a Steiner triple system of order with discrepancy . This is not true for , but we are able to asymptotically characterise all 2‐colourings which do not contain a Steiner triple system with high discrepancy. The key step in our proofs is a characterisation of 3‐uniform hypergraphs avoiding a certain natural type of induced subgraphs, contributing to the structural theory of hypergraphs. 10.1002/jcd.22004 http://creativecommons.org/licenses/by/4.0/ |
| doi_str_mv | 10.1002/jcd.22004 |
| format | Artículo Open Access |
| id | wiley_oa_10_1002_jcd_22004 |
| institution | Wiley Open Access |
| license_str_mv | http://creativecommons.org/licenses/by/4.0/ |
| publishDate | 2025 |
| publisher | Wiley |
| record_format | wiley_oa |
| spellingShingle | Steiner Triple Systems With High Discrepancy Lior Gishboliner Stefan Glock Amedeo Sgueglia Journal of Combinatorial Designs Steiner Triple Systems With High Discrepancy Lior Gishboliner Stefan Glock Amedeo Sgueglia Journal of Combinatorial Designs ABSTRACT In this paper, we initiate the study of discrepancy questions for combinatorial designs. Specifically, we show that, for every fixed and , any ‐colouring of the triples on admits a Steiner triple system of order with discrepancy . This is not true for , but we are able to asymptotically characterise all 2‐colourings which do not contain a Steiner triple system with high discrepancy. The key step in our proofs is a characterisation of 3‐uniform hypergraphs avoiding a certain natural type of induced subgraphs, contributing to the structural theory of hypergraphs. 10.1002/jcd.22004 http://creativecommons.org/licenses/by/4.0/ |
| title | Steiner Triple Systems With High Discrepancy |
| topic | Journal of Combinatorial Designs |
| url | https://onlinelibrary.wiley.com/doi/10.1002/jcd.22004 |