Minors for alternating dimaps

Abstract We develop a theory of minors for alternating dimaps—orientably embedded digraphs where, at each vertex, the incident edges (taken in the order given by the embedding) are directed alternately into, and out of, the vertex. We show that they are related by the triality relation of Tutte. The...

Full description

Saved in:
Bibliographic Details
Published in:Quarterly journal of mathematics 2018-03, Vol.69 (1), p.285-320
Main Author: Farr, G E
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c267t-f3cf54c3739381392c5d3b331c5b96203901f22b4c453a2858e8b5587a38cdc93
cites cdi_FETCH-LOGICAL-c267t-f3cf54c3739381392c5d3b331c5b96203901f22b4c453a2858e8b5587a38cdc93
container_end_page 320
container_issue 1
container_start_page 285
container_title Quarterly journal of mathematics
container_volume 69
creator Farr, G E
description Abstract We develop a theory of minors for alternating dimaps—orientably embedded digraphs where, at each vertex, the incident edges (taken in the order given by the embedding) are directed alternately into, and out of, the vertex. We show that they are related by the triality relation of Tutte. They do not commute in general, though do in many circumstances, and we characterize the situations where they do. We give a characterization of alternating dimaps of at most a given genus, using a finite set of excluded minors. We also use the minor operations to define simple Tutte invariants for alternating dimaps and characterize them. We establish a connection with the Tutte polynomial, and pose the problem of characterizing universal Tutte-like invariants for alternating dimaps based on these minor operations.
doi_str_mv 10.1093/qmath/hax039
format article
fullrecord <record><control><sourceid>oup_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1093_qmath_hax039</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><oup_id>10.1093/qmath/hax039</oup_id><sourcerecordid>10.1093/qmath/hax039</sourcerecordid><originalsourceid>FETCH-LOGICAL-c267t-f3cf54c3739381392c5d3b331c5b96203901f22b4c453a2858e8b5587a38cdc93</originalsourceid><addsrcrecordid>eNp9jz1PwzAURS0EEqGwsSJlY8H02c-fI6ooIBWxwGw5TkyD2iTYQYJ_TyDMTHc5ujqHkHMG1wwsLt_3ftwut_4T0B6QggklKBqhD0kBgEilAnVMTnJ-A2BKGF2Qi8e261MuY59Kvxub1Pmx7V7Lut37IZ-So-h3uTn72wV5Wd8-r-7p5unuYXWzoYErPdKIIUoRUKNFw9DyIGusEFmQlVV8sgEWOa9EEBI9N9I0ppLSaI8m1MHiglzNvyH1OacmuiFNAunLMXA_ae43zc1pE3454_3H8D_5DT92Tyk</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Minors for alternating dimaps</title><source>Oxford Journals Online</source><creator>Farr, G E</creator><creatorcontrib>Farr, G E</creatorcontrib><description>Abstract We develop a theory of minors for alternating dimaps—orientably embedded digraphs where, at each vertex, the incident edges (taken in the order given by the embedding) are directed alternately into, and out of, the vertex. We show that they are related by the triality relation of Tutte. They do not commute in general, though do in many circumstances, and we characterize the situations where they do. We give a characterization of alternating dimaps of at most a given genus, using a finite set of excluded minors. We also use the minor operations to define simple Tutte invariants for alternating dimaps and characterize them. We establish a connection with the Tutte polynomial, and pose the problem of characterizing universal Tutte-like invariants for alternating dimaps based on these minor operations.</description><identifier>ISSN: 0033-5606</identifier><identifier>EISSN: 1464-3847</identifier><identifier>DOI: 10.1093/qmath/hax039</identifier><language>eng</language><publisher>Oxford University Press</publisher><ispartof>Quarterly journal of mathematics, 2018-03, Vol.69 (1), p.285-320</ispartof><rights>2017. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oup.com 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c267t-f3cf54c3739381392c5d3b331c5b96203901f22b4c453a2858e8b5587a38cdc93</citedby><cites>FETCH-LOGICAL-c267t-f3cf54c3739381392c5d3b331c5b96203901f22b4c453a2858e8b5587a38cdc93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Farr, G E</creatorcontrib><title>Minors for alternating dimaps</title><title>Quarterly journal of mathematics</title><description>Abstract We develop a theory of minors for alternating dimaps—orientably embedded digraphs where, at each vertex, the incident edges (taken in the order given by the embedding) are directed alternately into, and out of, the vertex. We show that they are related by the triality relation of Tutte. They do not commute in general, though do in many circumstances, and we characterize the situations where they do. We give a characterization of alternating dimaps of at most a given genus, using a finite set of excluded minors. We also use the minor operations to define simple Tutte invariants for alternating dimaps and characterize them. We establish a connection with the Tutte polynomial, and pose the problem of characterizing universal Tutte-like invariants for alternating dimaps based on these minor operations.</description><issn>0033-5606</issn><issn>1464-3847</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp9jz1PwzAURS0EEqGwsSJlY8H02c-fI6ooIBWxwGw5TkyD2iTYQYJ_TyDMTHc5ujqHkHMG1wwsLt_3ftwut_4T0B6QggklKBqhD0kBgEilAnVMTnJ-A2BKGF2Qi8e261MuY59Kvxub1Pmx7V7Lut37IZ-So-h3uTn72wV5Wd8-r-7p5unuYXWzoYErPdKIIUoRUKNFw9DyIGusEFmQlVV8sgEWOa9EEBI9N9I0ppLSaI8m1MHiglzNvyH1OacmuiFNAunLMXA_ae43zc1pE3454_3H8D_5DT92Tyk</recordid><startdate>20180301</startdate><enddate>20180301</enddate><creator>Farr, G E</creator><general>Oxford University Press</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180301</creationdate><title>Minors for alternating dimaps</title><author>Farr, G E</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c267t-f3cf54c3739381392c5d3b331c5b96203901f22b4c453a2858e8b5587a38cdc93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Farr, G E</creatorcontrib><collection>CrossRef</collection><jtitle>Quarterly journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Farr, G E</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Minors for alternating dimaps</atitle><jtitle>Quarterly journal of mathematics</jtitle><date>2018-03-01</date><risdate>2018</risdate><volume>69</volume><issue>1</issue><spage>285</spage><epage>320</epage><pages>285-320</pages><issn>0033-5606</issn><eissn>1464-3847</eissn><abstract>Abstract We develop a theory of minors for alternating dimaps—orientably embedded digraphs where, at each vertex, the incident edges (taken in the order given by the embedding) are directed alternately into, and out of, the vertex. We show that they are related by the triality relation of Tutte. They do not commute in general, though do in many circumstances, and we characterize the situations where they do. We give a characterization of alternating dimaps of at most a given genus, using a finite set of excluded minors. We also use the minor operations to define simple Tutte invariants for alternating dimaps and characterize them. We establish a connection with the Tutte polynomial, and pose the problem of characterizing universal Tutte-like invariants for alternating dimaps based on these minor operations.</abstract><pub>Oxford University Press</pub><doi>10.1093/qmath/hax039</doi><tpages>36</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0033-5606
ispartof Quarterly journal of mathematics, 2018-03, Vol.69 (1), p.285-320
issn 0033-5606
1464-3847
language eng
recordid cdi_crossref_primary_10_1093_qmath_hax039
source Oxford Journals Online
title Minors for alternating dimaps
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T13%3A42%3A38IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-oup_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Minors%20for%20alternating%20dimaps&rft.jtitle=Quarterly%20journal%20of%20mathematics&rft.au=Farr,%20G%20E&rft.date=2018-03-01&rft.volume=69&rft.issue=1&rft.spage=285&rft.epage=320&rft.pages=285-320&rft.issn=0033-5606&rft.eissn=1464-3847&rft_id=info:doi/10.1093/qmath/hax039&rft_dat=%3Coup_cross%3E10.1093/qmath/hax039%3C/oup_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c267t-f3cf54c3739381392c5d3b331c5b96203901f22b4c453a2858e8b5587a38cdc93%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_oup_id=10.1093/qmath/hax039&rfr_iscdi=true