Christian Bey
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Quadratic LYM-type inequalities for intersecting Sperner families
dmtcs:3418 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2005,
DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
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https://doi.org/10.46298/dmtcs.3418
Quadratic LYM-type inequalities for intersecting Sperner families
Authors: Christian Bey 1
NULL
Christian Bey
1 Otto-von-Guericke-Universität Magdeburg = Otto-von-Guericke University [Magdeburg]
Let $\mathcal{F}\subseteq 2^{[n]}$ be a intersecting Sperner family (i.e. $A \not\subset B, A \cap B \neq \emptyset$ for all $A,B \in \mathcal{F}$) with profile vector $(f_i)_{i=0 \ldots n}$ (i.e. $f_i=|\mathcal{F} \cap \binom{[n]}{i}|$). We present quadratic inequalities in the $f_i$'s which sharpen the previously known linear $\mathrm{LYM}$-type inequalities.