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References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt145",{id:"formSmash:upper:j_idt145",widgetVar:"widget_formSmash_upper_j_idt145",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt146_j_idt148",{id:"formSmash:upper:j_idt146:j_idt148",widgetVar:"widget_formSmash_upper_j_idt146_j_idt148",target:"formSmash:upper:j_idt146:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

The k-assignment Polytope and the Space of Evolutionary TreesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2004 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Matematiska institutionen , 2004. , 68 p.
##### Series

Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1117
##### Keyword [en]

k-assignment, polytope, Birkhoff polytope, bipartite graphs
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-5677Local ID: LiU-TEK-LIC-2004:46ISBN: 91-85295-45-0OAI: oai:DiVA.org:liu-5677DiVA: diva2:21437
##### Presentation

2004-10-26, 00:00 (English)
#####

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#####

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Available from: 2005-03-09 Created: 2005-03-09 Last updated: 2013-11-14Bibliographically approved
##### List of papers

This thesis consists of two papers.

The first paper is a study of the structure of the k-assignment polytope, whose vertices are the *m x n* (0; 1)-matrices with exactly *k* 1:s and at most one 1 in each row and each column. This is a natural generalisation of the Birkhoff polytope and many of the known properties of the Birkhoff polytope are generalised. Two equivalent representations of the faces are given, one as (0; 1)-matrices and one as ear decompositions of bipartite graphs. These tools are used to describe properties of the polytope, especially a complete description of the cover relation in the face lattice of the polytope and an exact expression for the diameter.

The second paper studies the edge-product space *Є(X)* for trees on *X*. This space is generated by the set of edge-weighted finite trees on *X*, and arises by multiplying the weights of edges on paths in trees. These spaces are closely connected to tree-indexed Markov processes in molecular evolutionary biology. It is known that *Є(X)* has a natural *CW*-complex structure, and a combinatorial description of the associated face poset exists which is a poset *S(X)* of *X*-forests. In this paper it is shown that the edge-product space is a regular cell complex. One important part in showing that is to conclude that all intervals *[Ô, Г], Г *Є* S(X),* have recursive coatom orderings.

1. The k-assignment polytope$(function(){PrimeFaces.cw("OverlayPanel","overlay210918",{id:"formSmash:j_idt423:0:j_idt427",widgetVar:"overlay210918",target:"formSmash:j_idt423:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. A regular decomposition of the edge-product space of phylogenetic trees$(function(){PrimeFaces.cw("OverlayPanel","overlay214014",{id:"formSmash:j_idt423:1:j_idt427",widgetVar:"overlay214014",target:"formSmash:j_idt423:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1080",{id:"formSmash:lower:j_idt1080",widgetVar:"widget_formSmash_lower_j_idt1080",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1081_j_idt1083",{id:"formSmash:lower:j_idt1081:j_idt1083",widgetVar:"widget_formSmash_lower_j_idt1081_j_idt1083",target:"formSmash:lower:j_idt1081:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});