Ramon I. Garcia

activity

20212026

most citedIntersecting families of sets are typically trivial

1 citations · 1 across the 5 of their papers we have counts for

collaborators

7 papers

math.CO2026

Counting hypergraphs without linear cycles of fixed length

József Balogh, Ramon I. Garcia, Abhishek Methuku

Let $C_{k}^{(r)}$ be the $r$ -uniform linear cycle on $k$ hyperedges. An $r$ -graph is $C_{k}^{(r)}$ -free if it contains no copy of $C_{k}^{(r)}$ . Let $\operatorname{ex}_{r}(n,C_{k}^…

math.CO2026

Even smaller universal posets

József Balogh, Ramon I. Garcia, Marcelo Sales

We show that for every $η > 0$ and sufficiently large $n$ , there exists a poset of size $2^{(1 + η) n /2}$ containing all the $n$ -element posets as induced subposets. This improves a rec…

math.CO2025

Infinitely many groups exhibiting intermediate growth in maximal sum-free sets

József Balogh, Ramon I. Garcia, Hong Liu +1

Given an Abelian groups $G$ , denote $μ (G)$ the size of its largest sum-free subset and $f_{m a x} (G)$ the number of maximal sum-free sets in $G$ . Confirming a prediction by Liu and…

math.CO2025

Maximal independent sets in the middle two layers of the Boolean lattice

József Balogh, Ce Chen, Ramon I. Garcia

Let $B (2 d - 1, d)$ be the subgraph of the hypercube $Q_{2 d - 1}$ induced by its two largest layers. Duffus, Frankl and Rödl proposed the problem of finding the asymptotics fo…

math.CO2024

On the number of $P$ -free set systems for tree posets $P$

József Balogh, Ramon I. Garcia, Michael C. Wigal

We say a finite poset $P$ is a tree poset if its Hasse diagram is a tree. Let $k$ be the length of the largest chain contained in $P$ . We show that when $P$ is a fixed tree poset,…

math.CO2021★ 1 cited

Intersecting families of sets are typically trivial

József Balogh, Ramon I. Garcia, Lina Li +1

A family of subsets of $[n]$ is intersecting if every pair of its sets intersects. Determining the structure of large intersecting families is a central problem in extremal combina…

math.CO2021

On the number of sum-free triplets of sets

Igor Araujo, József Balogh, Ramon I. Garcia

We count the ordered sum-free triplets of subsets in the group $Z / p Z$ , i.e., the triplets $(A, B, C)$ of sets $A, B, C \subset Z / p Z$ for which the e…