Cubes of symmetric designs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914059453988864 |
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| author | Krčadinac, Vedran Pavčević, Mario Osvin Tabak, Kristijan |
| author_facet | Krčadinac, Vedran Pavčević, Mario Osvin Tabak, Kristijan |
| contents | We study $n$-dimensional matrices with $\{0,1\}$-entries ($n$-cubes) such that all their $2$-dimensional slices are incidence matrices of symmetric designs. A known construction of these objects obtained from difference sets is generalized so that the resulting $n$-cubes may have inequivalent slices. For suitable parameters, they can be transformed into $n$-dimensional Hadamard matrices with this property. In contrast, previously known constructions of $n$-dimensional designs all give examples with equivalent slices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_05446 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cubes of symmetric designs Krčadinac, Vedran Pavčević, Mario Osvin Tabak, Kristijan Combinatorics 05B05, 05B10, 05B20 We study $n$-dimensional matrices with $\{0,1\}$-entries ($n$-cubes) such that all their $2$-dimensional slices are incidence matrices of symmetric designs. A known construction of these objects obtained from difference sets is generalized so that the resulting $n$-cubes may have inequivalent slices. For suitable parameters, they can be transformed into $n$-dimensional Hadamard matrices with this property. In contrast, previously known constructions of $n$-dimensional designs all give examples with equivalent slices. |
| title | Cubes of symmetric designs |
| topic | Combinatorics 05B05, 05B10, 05B20 |
| url | https://arxiv.org/abs/2304.05446 |