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.
Fano kaleidoscopes and their generalizations / Buratti, Marco; Merola, Francesca. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - 87:4(2019), pp. 769-784. [10.1007/s10623-018-0538-6]
Fano kaleidoscopes and their generalizations
Marco Buratti;
2019
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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