The neighbors planted four types of herbs: basil, thyme, rosemary, and oregano. They planted the same number of each herb, and the total number of plants is 52.
To find out how many plants of each type there are, divide the total number of plants by the number of different types of herbs:
\[ \text{Number of each herb} = \frac{52}{4} = 13 \]
Therefore, the number of rosemary plants planted is 13.
So, the answer is 13 rosemary plants.