Sam Spiro

works on

additive combinatorics 1 extremal combinatorics 1 generalized turán problems 1 hypergraph independent sets 1 supersaturation 1

From the 1 of 16 linked papers with an AI index.

activity

20242026

collaborators

Showing 2025Show all

7 papers · 1 filter

math.CO2025

Tree Posets: Supersaturation, Enumeration, and Randomness

Tao Jiang, Sean Longbrake, Sam Spiro +1

We develop a powerful tool for embedding any tree poset $P$ of height $k$ in the Boolean lattice which allows us to solve several open problems in the area. We show that: * If $H$ …

math.CO2025

Rainbow Trees in Hypercubes

Nicholas Crawford, Maya Sankar, Carl Schildkraut +1

We prove that every proper edge-coloring of the $n$ -dimensional hypercube $Q_{n}$ contains a rainbow copy of every tree $T$ on at most $n$ edges. This result is best possible, as $Q_…

math.CO2025

Rational Exponents for General Graphs

Sean English, Sam Spiro

A rational number $r$ is a \textbf{realizable exponent} for a graph $H$ if there exists a finite family of graphs $F$ such that $ex (n, H, F) = I^ (n^{r})$ , wh…

math.CO2025

Sidorenko Hypergraphs and Random TurÃ¡n Numbers

Jiaxi Nie, Sam Spiro

Let $ex (G_{n, p}^{r}, F)$ denote the maximum number of edges in an $F$ -free subgraph of the random $r$ -uniform hypergraph $G_{n, p}^{r}$ , and let $s(F):=\sup\{s: \exists H,\ t_F(…

math.CO2025

Supersaturation of odd linear cycles

Lirong Deng, Jie Han, Jiaxi Nie +1

An $r$ -uniform linear cycle of length $ℓ$ , denoted by $C_{ℓ}^{r}$ , is an $r$ -graph with $ℓ$ edges $e_{1}, e_{2}, \dots, e_{ℓ}$ where $e_i=\{v_{(r-1)(i-1)},v_{(r-1)(i-1)+1},\dots…

math.CO2025

Random Polynomial Graphs for Random TurÃ¡n Problems

Sam Spiro

Bukh and Conlon used random polynomial graphs to give effective lower bounds on $ex (n, T^{ℓ})$ , where $T^{ℓ}$ is the $ℓ$ th power of a balanced root…