How to define JSON Schema for Map<String, Integer>?

You can:

{
  "type": "object",
  "properties": {
    "itemType": {"$ref": "#/definitions/mapInt"},
    "itemCount": {"$ref": "#/definitions/mapInt"}
  },
  "definitions": {
    "mapInt": {
      "type": "object",
      "additionalProperties": {"type": "integer"}
    }
  }
}