Geodesic
Coordinate deletion of zeroes
Eero Räty1
1University of Cambridge
The electronic journal of combinatorics, Tome 26 (2019) no. 3
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For a family $A\subseteq\left\{ 0,\dots,k\right\} ^{n}$, define the $\delta$-shadow of $A$ to be the set obtained from $A$ by removing from any of its vectors one coordinate that equals zero. Given the size of $A$, how should we choose $A$ to minimise its $\delta$-shadow? Our aim in this paper is to show that, for any $r$, the family of all sequences with at most $r$ zeros has minimal $\delta$-shadow. We actually give the exact best $A$ for every size.
DOI : 10.37236/8490
Classification : 05D05
Mots-clés : Kruskal-Katona theorem, lower shadow

Eero Räty  1

1 University of Cambridge 
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     author = {Eero R\"aty},
     title = {Coordinate deletion of zeroes},
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     year = {2019},
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     number = {3},
     doi = {10.37236/8490},
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Eero Räty. Coordinate deletion of zeroes. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8490

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