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(mod6), v≠ 13. 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.
Buratti, M., Merola, F. (2019). Fano Kaleidoscopes and their generalizations. DESIGNS, CODES AND CRYPTOGRAPHY, 87(4), 769-784 [10.1007/s10623-018-0538-6].
Fano Kaleidoscopes and their generalizations
BURATTI, MARCO;Merola, Francesca
2019-01-01
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(mod6), v≠ 13. 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.File | Dimensione | Formato | |
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