{"id":185889,"date":"2011-01-26T00:00:00","date_gmt":"2011-01-28T15:15:15","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/msr-research-item\/a-master-bijection-for-planar-maps-and-its-applications\/"},"modified":"2024-10-02T11:15:49","modified_gmt":"2024-10-02T18:15:49","slug":"a-master-bijection-for-planar-maps-and-its-applications","status":"publish","type":"msr-video","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/video\/a-master-bijection-for-planar-maps-and-its-applications\/","title":{"rendered":"A Master Bijection for Planar Maps, and Its Applications"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Planar maps are embeddings of connected planar graphs in the plane considered up to continuous deformation. We will present a \u201cmaster bijection\u201d for planar maps and show that it can be specialized in various ways in order to count several families of maps. More precisely, for each integer d we obtain a bijection between the family of maps of girth d and a family of decorated plane trees. This gives new counting results for maps of girth d counted according to the degree distribution of their faces. Our approach unifies and extends many known bijections. A key ingredient in the proofs are classes of orientations generalizing Schnyder woods.<\/p>\n<p>This is a joint work with Eric Fusy.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Planar maps are embeddings of connected planar graphs in the plane considered up to continuous deformation. We will present a \u201cmaster bijection\u201d for planar maps and show that it can be specialized in various ways in order to count several families of maps. More precisely, for each integer d we obtain a bijection between the [&hellip;]<\/p>\n","protected":false},"featured_media":195971,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[13546],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-185889","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-computational-sciences-mathematics","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/9cKUFIz896Y","msr_secondary_video_url":"","msr_video_file":"http:\/\/0","_links":{"self":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/185889","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":1,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/185889\/revisions"}],"predecessor-version":[{"id":1089804,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/185889\/revisions\/1089804"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/media\/195971"}],"wp:attachment":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/media?parent=185889"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=185889"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=185889"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=185889"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=185889"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=185889"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=185889"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=185889"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=185889"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=185889"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}