{"id":339737,"date":"2016-12-20T15:10:33","date_gmt":"2016-12-20T23:10:33","guid":{"rendered":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/?post_type=msr-research-item&p=339737"},"modified":"2018-10-16T21:16:34","modified_gmt":"2018-10-17T04:16:34","slug":"symmetric-1-dependent-colorings-integers","status":"publish","type":"msr-research-item","link":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/publication\/symmetric-1-dependent-colorings-integers\/","title":{"rendered":"Symmetric 1 – Dependent Colorings of the Integers"},"content":{"rendered":"

In a recent paper by the same authors, we constructed a stationary 1\u2212dependent 4\u2212coloring of the integers that is invariant under permutations of the colors. This was the first stationary k<\/em>\u2212dependent q<\/em>\u2212coloring for any k<\/em> and q<\/em>. When the analogous construction is carried out for q<\/em> > 4 colors, the resulting process is not k<\/em>\u2212dependent for any k<\/em>. We construct here a process that is symmetric in the colors and 1\u2212dependent for every q<\/em> \u2265 4. The construction uses a recursion involving Chebyshev polynomials evaluated at \u221a q\/2.<\/p>\n","protected":false},"excerpt":{"rendered":"

In a recent paper by the same authors, we constructed a stationary 1\u2212dependent 4\u2212coloring of the integers that is invariant under permutations of the colors. This was the first stationary k\u2212dependent q\u2212coloring for any k and q. When the analogous construction is carried out for q > 4 colors, the resulting process is not k\u2212dependent […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Institute of Mathematical Statistics","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Electronic Communications in Probability","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"20","msr_copyright":"","msr_conference_name":"","msr_doi":"10.1214\/ECP.v20-4070","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2015-03-19","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"http:\/\/projecteuclid.org\/euclid.ecp\/1465320958","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":0,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13546],"msr-publication-type":[193715],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-339737","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-computational-sciences-mathematics","msr-locale-en_us"],"msr_publishername":"Institute of Mathematical Statistics","msr_edition":"","msr_affiliation":"","msr_published_date":"2015-03-19","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"Electronic Communications in Probability","msr_volume":"20","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"339743","msr_publicationurl":"http:\/\/projecteuclid.org\/euclid.ecp\/1465320958","msr_doi":"10.1214\/ECP.v20-4070","msr_publication_uploader":[{"type":"file","title":"symcol","viewUrl":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-content\/uploads\/2016\/12\/symcol.pdf","id":339743,"label_id":0},{"type":"url","title":"http:\/\/projecteuclid.org\/euclid.ecp\/1465320958","viewUrl":false,"id":false,"label_id":0},{"type":"doi","title":"10.1214\/ECP.v20-4070","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[{"id":0,"url":"http:\/\/projecteuclid.org\/euclid.ecp\/1465320958"}],"msr-author-ordering":[{"type":"user_nicename","value":"holroyd","user_id":32020,"rest_url":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=holroyd"},{"type":"text","value":"Thomas M. 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