# Morrison, Natasha

## Weak saturation of the cube in the clique ★

**Problem**

Determine .

Keywords: bootstrap percolation; hypercube; Weak saturation

## Extremal $4$-Neighbour Bootstrap Percolation in the Hypercube ★★

**Problem**Determine the smallest percolating set for the -neighbour bootstrap process in the hypercube.

Keywords: bootstrap percolation; extremal combinatorics; hypercube; percolation

## Saturation in the Hypercube ★★

Author(s): Morrison; Noel; Scott

**Question**What is the saturation number of cycles of length in the -dimensional hypercube?

Keywords: cycles; hypercube; minimum saturation; saturation

## Saturated $k$-Sperner Systems of Minimum Size ★★

Author(s): Morrison; Noel; Scott

**Question**Does there exist a constant and a function such that if , then every saturated -Sperner system has cardinality at least ?

Keywords: antichain; extremal combinatorics; minimum saturation; saturation; Sperner system