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changed mathbb to mathcal
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domotorp
domotorp
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Let $X$ be an $n$-element set and $\mathbb{F} \subseteq P(X)$$\mathcal{F} \subseteq P(X)$ such that for all $A, B \in \mathbb{F}$$A, B \in \mathcal{F}$, $|A△B| \leq k$ where $A△B$ denotes the symmetric difference of $A$ and $B$. Suppose $|\mathbb{F}| = l$$|\mathcal{F}| = l$ for some $2 \leq l \leq 2^{n−1}$, then for what kind of $\mathbb{F}$$\mathcal{F}$ will the $|N(\mathbb{F})|$$|N(\mathcal{F})|$ be maximum, where $N(\mathbb{F}) = \{C \in P(X)\backslash \mathbb{F} : |C△A| ≤ k$$N(\mathcal{F}) = \{C \in P(X)\backslash \mathcal{F} : |C△A| ≤ k$, for all $A ∈ \mathbb{F}\}$$A ∈ \mathcal{F}\}$.

Let $X$ be an $n$-element set and $\mathbb{F} \subseteq P(X)$ such that for all $A, B \in \mathbb{F}$, $|A△B| \leq k$ where $A△B$ denotes the symmetric difference of $A$ and $B$. Suppose $|\mathbb{F}| = l$ for some $2 \leq l \leq 2^{n−1}$, then for what kind of $\mathbb{F}$ will the $|N(\mathbb{F})|$ be maximum, where $N(\mathbb{F}) = \{C \in P(X)\backslash \mathbb{F} : |C△A| ≤ k$, for all $A ∈ \mathbb{F}\}$.

Let $X$ be an $n$-element set and $\mathcal{F} \subseteq P(X)$ such that for all $A, B \in \mathcal{F}$, $|A△B| \leq k$ where $A△B$ denotes the symmetric difference of $A$ and $B$. Suppose $|\mathcal{F}| = l$ for some $2 \leq l \leq 2^{n−1}$, then for what kind of $\mathcal{F}$ will the $|N(\mathcal{F})|$ be maximum, where $N(\mathcal{F}) = \{C \in P(X)\backslash \mathcal{F} : |C△A| ≤ k$, for all $A ∈ \mathcal{F}\}$.

improve title, add quantifier
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j.c.
j.c.
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Combinatorics and extremal set theory Families of subsets with pairwise symmetric differences of cardinality at most $k$

Let $X$ be an $n$-element set and $\mathbb{F} \subseteq P(X)$ such that for all $A, B \in \mathbb{F}$ with, $|A△B| \leq k$ where $A△B$ denotes the symmetric difference of $A$ and $B$. Suppose $|\mathbb{F}| = l$ for some $2 \leq l \leq 2^{n−1}$, then for what kind of $\mathbb{F}$ will the $|N(\mathbb{F})|$ be maximum, where $N(\mathbb{F}) = \{C \in P(X)\backslash \mathbb{F} : |C△A| ≤ k$, for all $A ∈ \mathbb{F}\}$.

Combinatorics and extremal set theory

Let $X$ be an $n$-element set and $\mathbb{F} \subseteq P(X)$ such that $A, B \in \mathbb{F}$ with $|A△B| \leq k$ where $A△B$ denotes the symmetric difference of $A$ and $B$. Suppose $|\mathbb{F}| = l$ for some $2 \leq l \leq 2^{n−1}$, then for what kind of $\mathbb{F}$ will the $|N(\mathbb{F})|$ be maximum, where $N(\mathbb{F}) = \{C \in P(X)\backslash \mathbb{F} : |C△A| ≤ k$, for all $A ∈ \mathbb{F}\}$.

Families of subsets with pairwise symmetric differences of cardinality at most $k$

Let $X$ be an $n$-element set and $\mathbb{F} \subseteq P(X)$ such that for all $A, B \in \mathbb{F}$, $|A△B| \leq k$ where $A△B$ denotes the symmetric difference of $A$ and $B$. Suppose $|\mathbb{F}| = l$ for some $2 \leq l \leq 2^{n−1}$, then for what kind of $\mathbb{F}$ will the $|N(\mathbb{F})|$ be maximum, where $N(\mathbb{F}) = \{C \in P(X)\backslash \mathbb{F} : |C△A| ≤ k$, for all $A ∈ \mathbb{F}\}$.

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Francis Raj S
Francis Raj S
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Combinatorics and extremal set theory

Let $X$ be an $n$-element set and $\mathbb{F} \subseteq P(X)$ such that $A, B \in \mathbb{F}$ with $|A△B| \leq k$ where $A△B$ denotes the symmetric difference of $A$ and $B$. Suppose $|\mathbb{F}| = l$ for some $2 \leq l \leq 2^{n−1}$, then for what kind of $\mathbb{F}$ will the $|N(\mathbb{F})|$ be maximum, where $N(\mathbb{F}) = \{C \in P(X)\backslash \mathbb{F} : |C△A| ≤ k$, for all $A ∈ \mathbb{F}\}$.