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});});

On a class of commutative algebras associated to graphsPrimeFaces.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}); 2016 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Stockholm: Department of Mathematics, Stockholm University , 2016. , 40 p.
##### National Category

Discrete Mathematics Algebra and Logic
##### Identifiers

URN: urn:nbn:se:su:diva-132987OAI: oai:DiVA.org:su-132987DiVA: diva2:956005
##### Presentation

2016-09-05, Sal 14, hus 5, Kräftriket, Stockholm, 13:00 (English)
##### Opponent

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##### Supervisors

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt395",{id:"formSmash:j_idt395",widgetVar:"widget_formSmash_j_idt395",multiple:true});
Available from: 2016-11-03 Created: 2016-08-28 Last updated: 2016-11-03Bibliographically approved
##### List of papers

In 2004 Alexander Postnikov and Boris Shapiro introduced a class of commutative algebras for non-directed graphs. There are two main types of such algebras, algebras of the first type count spanning trees and algebras of the second type count spanning forests. These algebras have a number of interesting properties including an explicit formula for their Hilbert series. In this thesis we mainly work with the second type of algebras, we discover more properties of the original algebra and construct a few generalizations. In particular we prove that the algebra counting forests depends only on graphical matroid of the graph and converse. Furthermore, its "K-theoretic" filtration reconstructs the whole graph. We introduse $t$ labelled algebras of a graph, their Hilbert series contains complete information about the Tutte polynomial of the initial graph. Finally we introduce similar algebras for hypergraphs. To do this, we define spanning forests and trees of a hypergraph and the corresponding "hypergraphical" matroid.

1. On Postnikov-Shapiro Algebras and their generalizations$(function(){PrimeFaces.cw("OverlayPanel","overlay952673",{id:"formSmash:j_idt432:0:j_idt436",widgetVar:"overlay952673",target:"formSmash:j_idt432:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. "K-theoretic" analog of Postnikov-Shapiro algebra distinguishes graphs$(function(){PrimeFaces.cw("OverlayPanel","overlay955998",{id:"formSmash:j_idt432:1:j_idt436",widgetVar:"overlay955998",target:"formSmash:j_idt432:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1101",{id:"formSmash:lower:j_idt1101",widgetVar:"widget_formSmash_lower_j_idt1101",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1102_j_idt1104",{id:"formSmash:lower:j_idt1102:j_idt1104",widgetVar:"widget_formSmash_lower_j_idt1102_j_idt1104",target:"formSmash:lower:j_idt1102:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});