Question: Palentown is a hamlet in a county named for a province of what nationality?

Context paragraphs:
Palentown, New York: Palentown is a hamlet in Ulster County, New York, United States.

Catharine, New York: Catharine is a town in Schuyler County, New York.  The population was 1,930 at the 2000 census.  The town is one of two in the county named after Catherine Montour, a Native American interpreter and leader in the area.  The Town of Catharine is in the southeast part of the county and is north of Elmira, New York.

Ulster County, New York: Ulster County is a county located in the U.S. state of New York.  As of the 2010 census, the population was 182,493.  The county seat is Kingston.  The county is named after the Irish province of Ulster.

Beaver River, New York: Beaver River is a hamlet that is six tenths of a mile square, at the east end of Stillwater Reservoir, in the town of Webb in Herkimer County, New York.  The hamlet is surrounded by the Adirondack Park.  The hamlet has a year-round population of eight, that increases during the summer as many people have camps in this wilderness area.  There are 125 private properties, and three commercial businesses.  No roads lead to the hamlet; it is accessible only by hiking, rail car or boat in the summer and by snowmobile, snowshoes or cross country skis in the winter.  There is no electrical service.  The town is named for the Beaver River.  The New York Central Railroad right of way, on the National Register of Historic Places passes through the hamlet; an existing bunkhouse is a part of the historic property.

Bag Limit: Bag Limit is a crime novel written by Steven F. Havill.  It is a first person view story of a reluctant sheriff of Posados County named Bill Gastner.

Olin's Covered Bridge: Olin's Bridge, or Olin Bridge, or Olin-Dewey Road Bridge is a covered bridge that carries Dewey Road over the Ashtabula River in Plymouth Township, Ashtabula County, Ohio, United States.  The bridge, one of currently 16 drivable bridges in the county, is a single span Town truss design, and is currently the only bridge in the county named for a family.  The Olin family has owned property next to the bridge since it was built.  Members of the Olin family also operate a small museum and gift shop just east of the bridge at the house previously owned by Joyce Grandbouche.  The bridge’s WGCB number is 35-04-03, and it is located approximately 3.6 mi (5.7 km) east of Ashtabula.

List of counties in Vermont: There are fourteen counties in the U.S. state of Vermont.  These counties together contain 255 political units, or places, including 237 towns, 9 cities, 5 unincorporated areas, and 4 gores.  Each county has a county seat, often referred to as a "shire town."  In 1779, Vermont had two counties.  The western side of the state was called Bennington County and the eastern was called Cumberland County.  In 1781, Cumberland County was separated into three counties in Vermont plus another county named Washington (not the same as the modern Washington County) that eventually became part of New Hampshire.  Today's Washington County was known as Jefferson County from its creation in 1810 until it was renamed in 1814.  Essex County, Orleans County, and Caledonia County are commonly referred to as the "Northeast Kingdom".

Montour, New York: Montour is a town in Schuyler County, New York, United States.  The population was 2,446 at the 2000 census.  The town is one of two towns in the county named after Catherine Montour.

Brighton, Alabama: Brighton is a city near Birmingham, Alabama, United States and located just east of Hueytown.  At the 2010 census the population was 2,945.  It is one of four cities in Jefferson County named after cities in Great Britain.  Many of its early settlers were of English descent and named the town after the English tourist and resort city of Brighton which is located on the English Channel.

North Bay Shore, New York: North Bay Shore is an unincorporated neighborhood on Long Island in the Town of Islip in Suffolk County, New York, United States.  The area is a suburb of New York City.  The hamlet of "North Bay Shore" is within the northern part of the CDP of Bay Shore, New York.  The census-designated place (CDP) named "North Bay Shore" is north of, and adjacent to, the hamlet named North Bay Shore.  The CDP of North Bay Shore contains the hamlet of Pine Aire and part of the hamlet of Brentwood.  The population of the North Bay Shore CDP was 18,944 at the time of the 2010 census.

Supporting paragraphs: Palentown, New York Ulster County, New York
Answer: Irish