How Many Cards Should You Lay Out in a Game of EvenQuads: A Detailed Study of Caps in $$\textrm{AG}(n,2)$$
Julia Crager
1
,
Felicia Flores
1
,
Timothy E. Goldberg
2
,
Lauren L. Rose
1
,
Daniel Rose-Levine
1
,
Darrion Thornburgh
1
,
Raphael Walker
3
1
Department of Mathematics, Bard College, Annandale-on-Hudson, USA
|
Publication type: Journal Article
Publication date: 2023-05-31
Abstract
We define a cap in the affine geometry $$\textrm{AG}(n,2)$$ to be a subset in which any collection of 4 points is in general position. In this paper, we classify, up to affine equivalence, all caps in $$\textrm{AG}(n,2)$$ of size $$k \le 9$$ . As a result, we obtain a complete characterization of caps in dimension $$n \le 6$$ , in particular complete and maximal caps. Since the EvenQuads card deck is a model for $$\textrm{AG}(6,2)$$ , as a consequence, we determine the probability that an arbitrary k-card layout contains a quad.
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Crager J. et al. How Many Cards Should You Lay Out in a Game of EvenQuads: A Detailed Study of Caps in $$\textrm{AG}(n,2)$$ // La Matematica. 2023. Vol. 2. No. 2. pp. 382-419.
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Crager J., Flores F., Goldberg T. E., Rose L. L., Rose-Levine D., Thornburgh D., Walker R. How Many Cards Should You Lay Out in a Game of EvenQuads: A Detailed Study of Caps in $$\textrm{AG}(n,2)$$ // La Matematica. 2023. Vol. 2. No. 2. pp. 382-419.
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RIS
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TY - JOUR
DO - 10.1007/s44007-023-00047-0
UR - https://doi.org/10.1007/s44007-023-00047-0
TI - How Many Cards Should You Lay Out in a Game of EvenQuads: A Detailed Study of Caps in $$\textrm{AG}(n,2)$$
T2 - La Matematica
AU - Crager, Julia
AU - Flores, Felicia
AU - Goldberg, Timothy E.
AU - Rose, Lauren L.
AU - Rose-Levine, Daniel
AU - Thornburgh, Darrion
AU - Walker, Raphael
PY - 2023
DA - 2023/05/31
PB - Springer Nature
SP - 382-419
IS - 2
VL - 2
SN - 2730-9657
ER -
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BibTex (up to 50 authors)
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@article{2023_Crager,
author = {Julia Crager and Felicia Flores and Timothy E. Goldberg and Lauren L. Rose and Daniel Rose-Levine and Darrion Thornburgh and Raphael Walker},
title = {How Many Cards Should You Lay Out in a Game of EvenQuads: A Detailed Study of Caps in $$\textrm{AG}(n,2)$$},
journal = {La Matematica},
year = {2023},
volume = {2},
publisher = {Springer Nature},
month = {may},
url = {https://doi.org/10.1007/s44007-023-00047-0},
number = {2},
pages = {382--419},
doi = {10.1007/s44007-023-00047-0}
}
Cite this
MLA
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Crager, Julia, et al. “How Many Cards Should You Lay Out in a Game of EvenQuads: A Detailed Study of Caps in $$\textrm{AG}(n,2)$$.” La Matematica, vol. 2, no. 2, May. 2023, pp. 382-419. https://doi.org/10.1007/s44007-023-00047-0.