We show that any affine block design D = (P, B) is a subset of a suitable commutative group G_D, with the property that a k-subset of P is a block of D if and only if its k elements sum up to zero. As a consequence, the group of automorphisms of any affine design D is the group of automorphisms of G_D that leave P invariant. Whenever k is a prime p, G_D is an elementary abelian p-group.
Caggegi, A., Falcone, G., & Pavone, M. (2020). Additivity of affine designs. JOURNAL OF ALGEBRAIC COMBINATORICS, 1-16.
Data di pubblicazione: | 2020 |
Titolo: | Additivity of affine designs |
Autori: | |
Citazione: | Caggegi, A., Falcone, G., & Pavone, M. (2020). Additivity of affine designs. JOURNAL OF ALGEBRAIC COMBINATORICS, 1-16. |
Rivista: | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s10801-020-00941-8 |
Abstract: | We show that any affine block design D = (P, B) is a subset of a suitable commutative group G_D, with the property that a k-subset of P is a block of D if and only if its k elements sum up to zero. As a consequence, the group of automorphisms of any affine design D is the group of automorphisms of G_D that leave P invariant. Whenever k is a prime p, G_D is an elementary abelian p-group. |
Settore Scientifico Disciplinare: | Settore MAT/03 - Geometria Settore MAT/05 - Analisi Matematica |
Appare nelle tipologie: | 1.01 Articolo in rivista |
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