Sam Spiro

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6 papers · 1 filter

math.CO2024

Random Turán Problems for $K_{s, t}$ Expansions

Jiaxi Nie, Sam Spiro

Let $K_{s, t}^{(r)}$ denote the $r$ -uniform hypergraph obtained from the graph $K_{s, t}$ by inserting $r - 2$ new vertices inside each edge of $K_{s, t}$ . We prove essentially tight bo…

math.CO2023

Eulerian Polynomials for Digraphs

Kyle Celano, Nicholas Sieger, Sam Spiro

Given an $n$ -vertex digraph $D$ and a labeling $σ : V (D) \to [n]$ , we say that an arc $u \to v$ of $D$ is a descent of $σ$ if $σ (u) > σ (v)$ . Foata and Zeilberger introduced a generating…

math.CO2023

The Random Turán Problem for Theta Graphs

Gwen McKinley, Sam Spiro

Given a graph $F$ , we define $ex (G_{n, p}, F)$ to be the maximum number of edges in an $F$ -free subgraph of the random graph $G_{n, p}$ . Very little is known about $\op…

math.CO2022

Zero Forcing with Random Sets

Bryan Curtis, Luyining Gan, Jamie Haddock +2

Given a graph $G$ and a real number $0 \leq p \leq 1$ , we define the random set $B_{p} (G) \subset V (G)$ by including each vertex independently and with probability $p$ . We investigate the…

math.CO2022

The Maximum Number of Appearances of a Word in a Grid

Gregory Patchell, Sam Spiro

How can you fill a $3 \times 3$ grid with the letters A and M so that the word ``AMM'' appears as many times as possible in the grid? More generally, given a word $w$ of length $n$ ,…

math.CO2022

Complementary Vanishing Graphs

Craig Erickson, Luyining Gan, Jürgen Kritschgau +2

Given a graph $G$ with vertices ${v_{1}, \dots, v_{n}}$ , we define $S (G)$ to be the set of symmetric matrices $A = [a_{i, j}]$ such that for $i \neq = j$ we have $a_{i, j} \neq = 0$ if…

Random Turán Problems for Ks,t​ Expansions

Eulerian Polynomials for Digraphs

The Random Turán Problem for Theta Graphs

Zero Forcing with Random Sets

The Maximum Number of Appearances of a Word in a Grid

Complementary Vanishing Graphs

Random Turán Problems for $K_{s, t}$ Expansions