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arXiv · 1801.02519

Fano Kaleidoscopes and their generalizations

Marco Buratti·Francesca Merola
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Abstract

In this work we introduce Fano Kaleidoscopes, Hesse Kaleidoscopes and their generalizations. These are a particular kind of colored designs for which we will discuss general theory, present some constructions and prove existence results. In particular, using difference methods we show the existence of both a Fano and a Hesse Kaleidoscope on $v$ points when $v$ is a prime or prime power congruent to 1$\pmod{6}$, $v\ne13$. In the Fano case this, together with known results on pairwise balanced designs, allows us to prove the existence of Kaleidoscopes of order $v$ for many other values of $v$; we discuss what the situation is, on the other hand, in the Hesse and general case.

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Marco Buratti, Francesca Merola. 2018-01-08. Fano Kaleidoscopes and their generalizations. https://arxiv.org/abs/1801.02519

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