Fano Kaleidoscopes and their generalizations
| Autor: | Francesca Merola, Marco Buratti |
|---|---|
| Přispěvatelé: | Buratti, Marco, Merola, Francesca |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Pairwise balanced design Applied Mathematics Colored design Order (ring theory) Computer Science Applications1707 Computer Vision and Pattern Recognition Colored designs Difference families Cyclotomy Pairwise balanced designs Fano plane Prime (order theory) Kaleidoscope Computer Science Applications Difference familie Pairwise balanced designs General theory FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) Colored designs Difference families Prime power computer Cyclotomy Mathematics computer.programming_language |
| Zdroj: | Designs, Codes and Cryptography. 87:769-784 |
| ISSN: | 1573-7586 0925-1022 |
| DOI: | 10.1007/s10623-018-0538-6 |
| Popis: | 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. 19 pages |
| Databáze: | OpenAIRE |
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