On circulant ternary coherent configurations of prime degree
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918455075143680 |
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| author | Chen, Gang Ren, Qing Ponomarenko, Ilia |
| author_facet | Chen, Gang Ren, Qing Ponomarenko, Ilia |
| contents | Ternary coherent configurations are, on the one hand, a special case of multidimensional coherent configurations introduced by L. Babai (2016), and, on the other hand, a natural generalization of association schemes on triples introduced by D. M. Mesner and P. Bhattacharya (1990). A ternary coherent configuration X is said to be circulant if the automorphism group Aut(X) of X has a regular cyclic subgroup, and schurian if the classes of X are the orbits of the componentwise action of the group Aut(X) on triples of points of X. It is proved that any circulant ternary coherent configuration X of prime degree p is schurian with the possible exception of the case when X is an association schemes on triples and either Aut(X) = AGL1(p) and p = +1, or -1 (mod 8), or Aut(X) is a proper subgrou of AGL1(p). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_17687 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On circulant ternary coherent configurations of prime degree Chen, Gang Ren, Qing Ponomarenko, Ilia Combinatorics Ternary coherent configurations are, on the one hand, a special case of multidimensional coherent configurations introduced by L. Babai (2016), and, on the other hand, a natural generalization of association schemes on triples introduced by D. M. Mesner and P. Bhattacharya (1990). A ternary coherent configuration X is said to be circulant if the automorphism group Aut(X) of X has a regular cyclic subgroup, and schurian if the classes of X are the orbits of the componentwise action of the group Aut(X) on triples of points of X. It is proved that any circulant ternary coherent configuration X of prime degree p is schurian with the possible exception of the case when X is an association schemes on triples and either Aut(X) = AGL1(p) and p = +1, or -1 (mod 8), or Aut(X) is a proper subgrou of AGL1(p). |
| title | On circulant ternary coherent configurations of prime degree |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.17687 |