How many cards should you lay out in a game of EvenQuads: a detailed study of caps in \(\mathrm{AG}(n, 2)\). (English) Zbl 1522.05025
In the paper under review, the authors consider sets \(\mathcal{O}\) of points in \(\mathrm{AG}(n, 2)\) such that any four points of \(\mathcal{O}\) are in general position. Equivalently, no affine plane is contained in \(\mathcal{O}\). All such sets of size at most \(9\) in \(\mathrm{AG}(n, 2)\) are classified, up to affine equivalence. Moreover, the complete and maximal sets of this type in \(\mathrm{AG}(n, 2)\), \(n \le 6\), are characterized.
Reviewer: Francesco Pavese (Bari)
MSC:
| 05B25 | Combinatorial aspects of finite geometries |
| 51E10 | Steiner systems in finite geometry |
| 51E15 | Finite affine and projective planes (geometric aspects) |
Keywords:
finite geometry; affine geometry; recreational mathematics; combinatorics; Sidon sets; caps; EvenQuadsOnline Encyclopedia of Integer Sequences:
Expansion of 1/((1-2x)(1-4x)(1-8x)).Number of magic quad squares that can be formed using cards from Quads-2^n deck, where the first row and column are fixed.
The number of magic quad squares that can be formed using cards from Quads-2^n deck.
Number of strongly magic quad squares that can be formed using cards from Quads-2^n deck.
Number of semimagic quads squares that can be formed using cards from Quads-2^n deck, where the first row and column are fixed.
Number of semimagic quad squares that can be formed using cards from Quads-2^n deck.
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