Kan. Stat. § 19-2784
That whenever a petition in conformity to the next preceding section and signed by not less than one-fourth (1/4) of the taxpayers residing within the area named in the petition, or signed by all of the owners within the area named in the petition if there be no resident taxpayers within such area, shall be presented to the county commissioners praying that the limits of the improvement district be extended to include within its boundaries the territory described in the petition it shall be the duty forthwith of such board of county commissioners to fix a time for a hearing of such petition and to cause the county clerk to give notice thereof by one publication in some newspaper published and of general circulation in the county, at least five (5) days before the day fixed for the hearing.
K.S.A. 19-2784