Let p1, p2, . . . , pn be pairwise coprime positive integers and let P = p1p2 · · · pn. Let 0,1,...,m−1 be a sequence of m different colors. Let A be an n×mP matrix of colors in which row i consists of blocks of pi consecutive entries of the same color, with colors 0 through m − 1 repeated cyclically. The Monochromatic Column problem is to determine the number of columns of A in which every entry is the same color. A partial solution for the case when m is prime is given.
","abstract_html":"<p>Let p1, p2, . . . , pn be pairwise coprime positive integers and let P = p1p2 · · · pn. Let 0,1,...,m−1 be a sequence of m different colors. Let A be an n×mP matrix of colors in which row i consists of blocks of pi consecutive entries of the same color, with colors 0 through m − 1 repeated cyclically. The Monochromatic Column problem is to determine the number of columns of A in which every entry is the same color. A partial solution for the case when m is prime is given. </p>","abstract_has_math":false,"creators":["Crowell, Loran Elizabeth"],"institution":"Eastern Kentucky University","degree_name":"Master of Arts (MA)","degree_level":"Master's","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-01-01T08:00:00Z","date_published":"2016-01-01T08:00:00Z","updated_at":"2026-07-24T02:15:32Z","subjects":["Chinese Remainder Theorem","Monochromatic Column","Number Theory"],"languages":[],"rights":["Copyright 2016 Loran Elizabeth Crowell"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://encompass.eku.edu/etd/356","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Crowell, Loran Elizabeth"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Encompass Digital Archive, Eastern Kentucky University"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts (MA)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Eastern Kentucky University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Chinese Remainder Theorem","Monochromatic Column","Number Theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2016 Loran Elizabeth Crowell"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://encompass.eku.edu/etd/356"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let p1, p2, . . . , pn be pairwise coprime positive integers and let P = p1p2 · · · pn. Let 0,1,...,m−1 be a sequence of m different colors. Let A be an n×mP matrix of colors in which row i consists of blocks of pi consecutive entries of the same color, with colors 0 through m − 1 repeated cyclically. The Monochromatic Column problem is to determine the number of columns of A in which every entry is the same color. A partial solution for the case when m is prime is given.
"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:source","label":"Dc Source","values":["Encompass Digital Archive: Online Theses and Dissertations"]},{"key":"dc:title","label":"Title","values":["The Monochromatic Column Problem: The Prime Case"]}]}],"canonical_facts":{"dc:creator":["Crowell, Loran Elizabeth"],"dc:description.abstract":["Let p1, p2, . . . , pn be pairwise coprime positive integers and let P = p1p2 · · · pn. Let 0,1,...,m−1 be a sequence of m different colors. Let A be an n×mP matrix of colors in which row i consists of blocks of pi consecutive entries of the same color, with colors 0 through m − 1 repeated cyclically. The Monochromatic Column problem is to determine the number of columns of A in which every entry is the same color. A partial solution for the case when m is prime is given.
"],"dc:format":["application/pdf"],"dc:identifier":["https://encompass.eku.edu/etd/356"],"dc:publisher":["Encompass Digital Archive, Eastern Kentucky University"],"dc:rights":["Copyright 2016 Loran Elizabeth Crowell"],"dc:source":["Encompass Digital Archive: Online Theses and Dissertations"],"dc:subject":["Chinese Remainder Theorem","Monochromatic Column","Number Theory"],"dc:title":["The Monochromatic Column Problem: The Prime Case"],"dc:type":["Master Thesis"],"thesis:degree_discipline":["Mathematics and Statistics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Arts (MA)"],"thesis:institution_name":["Eastern Kentucky University"]},"updated_at":"2026-07-24T02:15:32Z"}