Maria-Romina Ivan

activity

20202026

most citedMinimal Diamond-Saturated Families

11 citations · 46 across the 24 of their papers we have counts for

collaborators

25 papers

math.CO2026

The Bounded-Linear Dichotomy Holds for all 4 Point Posets

Maria-Romina Ivan, Sean Jaffe

Given a finite poset $P$ , its induced saturation number, $sat^{*} (n, P)$ is the smallest size a family of subsets of $[n]$ can have such that it does not cont…

math.AT2026

Antipodal paths in covers of spheres

David Ellis, Maria-Romina Ivan, Imre Leader +1

In this note we show that if the sphere $S^{n}$ is covered by $k$ open sets with $n \geq 2 k - 2$ , then one of these sets contains a path with antipodal endpoints. This is best…

math.CO2026

Generalised Prisms and Euclidean Ramsey Theory

Maria-Romina Ivan, Imre Leader, Mark Walters

A finite subset $X$ of $R^{d}$ is called Ramsey if for every $k$ there exists an $n$ such that whenever $R^{n}$ is $k$ -coloured there exists a monochromatic congruent c…

math.CO2026

The Exact Saturation Number for the Diamond

Maria-Romina Ivan, Sean Jaffe

What is the smallest size of a family of subsets of $[n]$ such that it does not contain an induced copy of $Q_{2}$ as a poset (known as the \textit{diamond}), but adding a new set cr…

math.CO2026

A New Lower Bound for the Diagonal Poset Ramsey Numbers

Maria-Romina Ivan, Bernardus A. Wessels

Given two finite posets $P$ and $Q$ , their Ramsey number, denoted by $R (P, Q)$ , is defined to be the smallest integer $N$ such that any blue/red…

math.CO2025

Linear Saturation for $N$ via Butterflies

Maria-Romina Ivan, Nandi Wang

Given a finite poset $P$ , how small can a family $F$ of subsets of $[n]$ be such that $F$ does not contain an induced copy of $P$ , but $\mathcal…

math.CO2025

Saturation for Sums of Posets and Antichains

Maria-Romina Ivan, Sean Jaffe

Given a finite poset $P$ , we say that a family $F$ of subsets of $[n]$ is $P$ -saturated if $F$ does not contain an induced copy of $P$ ,…

math.CO2025

Optimal Embeddings of Posets in Hypercubes

Tomáš Flídr, Maria-Romina Ivan, Sean Jaffe

Given a finite poset $P$ , the hypercube-height, denoted by $h^{*} (P)$ , is defined to be the minimum $h$ such that there exists a natural number $n$ for which the su…

math.CO2025

All Ordinals are Cop-Robber Ordinals

Jorge Cruz Chapital, Tomáš Flídr, Maria-Romina Ivan

The game of cops and robbers, played on a fixed graph $G$ , is a two-player game, where the cop and the robber (the players) take turns in moving to adjacent vertices. The game fini…

math.CO2025

A Cop-Win Graph with Maximum Capture Time $ω$

Tomáš Flídr, Maria-Romina Ivan

The game of cops and robbers is played on a fixed (finite or infinite) graph $G$ . The cop chooses his starting position, then the robber chooses his. After that, they take turns an…

math.CO2025

The Saturation Number for the Diamond is Linear

Maria-Romina Ivan, Sean Jaffe

For a fixed poset $P$ we say that a family $F \subseteq P ([n])$ is $P$ -saturated if it does not contain an induced copy of $P$ , but whene…

math.CO2025

Gluing Posets and the Dichotomy of Poset Saturation Numbers

Maria-Romina Ivan, Sean Jaffe

Given a finite poset $P$ , we say that a family $F$ of subsets of $[n]$ is $P$ -saturated if $F$ does not contain an induced copy of $P$ ,…

math.CO2025

The Maximum Number of Bases in a Family of Vectors

David Ellis, Maria-Romina Ivan, Imre Leader

The proportion of $d$ -element subsets of $F_{2}^{d}$ that are bases is asymptotic to $\prod_{j = 1}^{\infty} (1 - 2^{- j}) \approx 0.29$ as $d \to \infty$ . It is natural to ask whet…

math.CO2024

Turán Densities for Small Hypercubes

David Ellis, Maria-Romina Ivan, Imre Leader

How small can a set of vertices in the $n$ -dimensional hypercube $Q_{n}$ be if it meets every copy of $Q_{d}$ ? The asymptotic density of such a set (for $d$ fixed and $n$ large) is den…

math.CO2024

Block Sizes in the Block Sets Conjecture

Maria-Romina Ivan, Imre Leader, Mark Walters

A set $X$ is called Euclidean Ramsey if, for any $k$ and sufficiently large $n$ , every $k$ -colouring of $R^{n}$ contains a monochromatic congruent copy of $X$ . This notion w…

math.CO2024★ 10 cited

Turán Densities for Daisies and Hypercubes

David Ellis, Maria-Romina Ivan, Imre Leader

An $r$ -daisy is an $r$ -uniform hypergraph consisting of the six $r$ -sets formed by taking the union of an $(r - 2)$ -set with each of the 2-sets of a disjoint 4-set. Bollobás, Leader…

math.CO2023

A collection of open problems in celebration of Imre Leader's 60th birthday

Rahil Baber, Natalie Behague, Asier Calbet +10

One of the great pleasures of working with Imre Leader is to experience his infectious delight on encountering a compelling combinatorial problem. This collection of open problems…

math.CO2023★ 3 cited

A Polynomial Upper Bound for Poset Saturation

Paul Bastide, Carla Groenland, Maria-Romina Ivan +1

Given a finite poset $P$ , we say that a family $F$ of subsets of $[n]$ is $P$ -saturated if $F$ does not contain an induced copy of $P$ ,…

math.CO2022★ 1 cited

Some New Results on Monochromatic Sums and Products in the Rationals

Neil Hindman, Maria-Romina Ivan, Imre Leader

Our aim in this paper is to show that, for any $k$ , there is a finite colouring of the set of rationals whose denominators contain only the first $k$ primes such that no infinite s…

math.CO2022★ 5 cited

Saturation for Small Antichains

Irina Đanković, Maria-Romina Ivan

For a given positive integer $k$ we say that a family of subsets of $[n]$ is $k$ -antichain saturated if it does not contain $k$ pairwise incomparable sets, but whenever we add to i…

math.CO2022★ 4 cited

Constructible Graphs and Pursuit

Maria-Romina Ivan, Imre Leader, Mark Walters

A (finite or infinite) graph is called constructible if it may be obtained recursively from the one-point graph by repeatedly adding dominated vertices. In the finite case, the con…

math.CO2022★ 1 cited

Small Sets in Union-Closed Families

David Ellis, Maria-Romina Ivan, Imre Leader

Our aim in this note is to show that, for any $ε > 0$ , there exists a union-closed family $F$ with (unique) smallest set $S$ such that no element of $S$ belongs to more than…

math.CO2021★ 11 cited

Minimal Diamond-Saturated Families

Maria-Romina Ivan

For a given fixed poset $P$ we say that a family of subsets of $[n]$ is $P$ -saturated if it does not contain an induced copy of $P$ , but whenever we add…

math.CO2020

A Ramsey Characterisation of Eventually Periodic Words

Maria-Romina Ivan, Imre Leader, Luca Q. Zamboni

A factorisation $x = u_{1} u_{2} \dots$ of an infinite word $x$ on alphabet $X$ is called `monochromatic', for a given colouring of the finite words $X^{*}$ on alphabet $X$ , if each $u_…

The Bounded-Linear Dichotomy Holds for all 4 Point Posets

Antipodal paths in covers of spheres

Generalised Prisms and Euclidean Ramsey Theory

The Exact Saturation Number for the Diamond

A New Lower Bound for the Diagonal Poset Ramsey Numbers

Linear Saturation for N via Butterflies

Saturation for Sums of Posets and Antichains

Optimal Embeddings of Posets in Hypercubes

All Ordinals are Cop-Robber Ordinals

A Cop-Win Graph with Maximum Capture Time ω

The Saturation Number for the Diamond is Linear

Gluing Posets and the Dichotomy of Poset Saturation Numbers

The Maximum Number of Bases in a Family of Vectors

Turán Densities for Small Hypercubes

Block Sizes in the Block Sets Conjecture

Turán Densities for Daisies and Hypercubes

A collection of open problems in celebration of Imre Leader's 60th birthday

A Polynomial Upper Bound for Poset Saturation

Some New Results on Monochromatic Sums and Products in the Rationals

Saturation for Small Antichains

Constructible Graphs and Pursuit

Small Sets in Union-Closed Families

Minimal Diamond-Saturated Families

A Ramsey Characterisation of Eventually Periodic Words

Linear Saturation for $N$ via Butterflies

A Cop-Win Graph with Maximum Capture Time $ω$