A difference multiset in an additive group $G$ is a multiset $X=(x_1,\cdots,x_k)$ such that the list $\Delta X=(x_i-x_j\:\ 1\le i\le k,\ 1\le j\le k,\ i\ne j)$ contains each element (including 0) of $G$ the same number of times. Similarly, a strong difference family (SDF) is a family of multisets $X_1,\cdots,X_t$ such that the union of the lists $\Delta X_i$ contains each element of $G$ the same number of times. It is shown how useful these are in the construction of regular group divisible designs and regular or 1-rotational balanced incomplete block designs. Examples using Paley difference multisets or Paley SDFs are given, and many new resolvable 1-rotational designs are constructed.

Old and new designs via difference multisets and strong difference families

BURATTI, Marco
1999

Abstract

A difference multiset in an additive group $G$ is a multiset $X=(x_1,\cdots,x_k)$ such that the list $\Delta X=(x_i-x_j\:\ 1\le i\le k,\ 1\le j\le k,\ i\ne j)$ contains each element (including 0) of $G$ the same number of times. Similarly, a strong difference family (SDF) is a family of multisets $X_1,\cdots,X_t$ such that the union of the lists $\Delta X_i$ contains each element of $G$ the same number of times. It is shown how useful these are in the construction of regular group divisible designs and regular or 1-rotational balanced incomplete block designs. Examples using Paley difference multisets or Paley SDFs are given, and many new resolvable 1-rotational designs are constructed.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1654636
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