P. Frankl

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20112026

s

pairwise disjoint sets

15 citations · 86 across the 50 of their papers we have counts for

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Showing 2021 · math.COShow all

8 papers · 2 filters

math.CO2021

Piercing the chessboard

Gergely Ambrus, Imre Bárány, Péter Frankl +1

We consider the minimum number of lines $h_{n}$ and $p_{n}$ needed to intersect or pierce, respectively, all the cells of the $n \times n$ chessboard. Determining these values can also…

math.CO2021

On the maximum number of distinct intersections in an intersecting family

Peter Frankl, Sergei Kiselev, Andrey Kupavskii

For $n > 2 k \geq 4$ we consider intersecting families $F$ consisting of $k$ -subsets of ${1, 2, \dots, n}$ . Let $I (F)$ denote the family of all distinc…

math.CO2021

Best possible bounds on the number of distinct differences in intersecting families

Peter Frankl, Sergei Kiselev, Andrey Kupavskii

For a family $F$ , let $D (F)$ stand for the family of all sets that can be expressed as $F ∖ G$ , where $F, G \in F$ . A family $F$ i…

math.CO2021

Uniform intersecting families with large covering number

Peter Frankl, Andrey Kupavskii

A family $F$ has covering number $τ$ if the size of the smallest set intersecting all sets from $F$ is equal to $τ$ . Let $M (n, k, τ)$ stand for the size of the larg…

math.CO2021

On the sum of sizes of overlapping families

Peter Frankl, Jian Wang

Let $A_{1}, \dots, A_{m}$ be families of $k$ -subsets of an $n$ -set. Suppose that one cannot choose pairwise disjoint edges from $s + 1$ distinct families. Subject to t…

math.CO2021

Exchange properties of finite set-systems

Peter Frankl, János Pach, Dömötör Pálvölgyi

In a recent breakthrough, Adiprasito, Avvakumov, and Karasev constructed a triangulation of the $n$ -dimensional real projective space with a subexponential number of vertices. They…

math.CO2021

On well-connected sets of strings

Peter Frankl, Janos Pach

Given $n$ pairwise disjoint sets $X_{1}, \dots, X_{n}$ , we call the elements of $S = X_{1} \times \dots \times X_{n}$ strings. A nonempty set of strings $W \subseteq S$ is said to be well-conne…

math.CO2021★ 2 cited

On strengthenings of the intersecting shadow theorem

P. Frankl, G. O. H. Katona

Let $n > k > t \geq j \geq 1$ be integers. Let $X$ be an $n$ -element set, $(k X)$ the collection of its $k$ -subsets. A family $F \subset (k X)$ is called $t$ …