<?xml version="1.0" encoding="UTF-8"?><?xml-stylesheet type="text/xsl" href="static/style.xsl"?><OAI-PMH xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/ http://www.openarchives.org/OAI/2.0/OAI-PMH.xsd"><responseDate>2026-09-21T03:31:00Z</responseDate><request verb="GetRecord" identifier="oai:dspace.mit.edu:1721.1/38882" metadataPrefix="dim">https://dspace.mit.edu/server/oai/request</request><GetRecord><record><header><identifier>oai:dspace.mit.edu:1721.1/38882</identifier><datestamp>2022-01-13T07:54:35Z</datestamp><setSpec>com_1721.1_7582</setSpec><setSpec>com_1721.1_7581</setSpec><setSpec>col_1721.1_131022</setSpec></header><metadata><dim:dim xmlns:dim="http://www.dspace.org/xmlns/dspace/dim" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:doc="http://www.lyncode.com/xoai" xsi:schemaLocation="http://www.dspace.org/xmlns/dspace/dim http://www.dspace.org/schema/dim.xsd">
   <dim:field mdschema="dc" element="contributor" qualifier="advisor" lang="en_US">Richard P. Stanley.</dim:field>
   <dim:field mdschema="dc" element="contributor" qualifier="author" lang="en_US">Burns, Jason Matthew</dim:field>
   <dim:field mdschema="dc" element="contributor" qualifier="other" lang="en_US">Massachusetts Institute of Technology. Dept. of Mathematics.</dim:field>
   <dim:field mdschema="dc" element="contributor" qualifier="department">Massachusetts Institute of Technology. Department of Mathematics</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="accessioned">2007-09-27T19:30:34Z</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="available">2007-09-27T19:30:34Z</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="copyright" lang="en_US">2007</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="issued" lang="en_US">2007</dim:field>
   <dim:field mdschema="dc" element="identifier" qualifier="uri">http://hdl.handle.net/1721.1/38882</dim:field>
   <dim:field mdschema="dc" element="identifier" qualifier="oclc" lang="en_US">166267576</dim:field>
   <dim:field mdschema="dc" element="description" lang="en_US">Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.</dim:field>
   <dim:field mdschema="dc" element="description" lang="en_US">This electronic version was submitted by the student author.  The certified thesis is available in the Institute Archives and Special Collections.</dim:field>
   <dim:field mdschema="dc" element="description" lang="en_US">Includes bibliographical references (leaves 60-62).</dim:field>
   <dim:field mdschema="dc" element="description" qualifier="abstract" lang="en_US">We give nontrivial upper and lower bounds for the total number of distinct degree sequences among all simple, unlabeled graphs on n vertices (graphical partitions on n vertices). Our upper bound is ... for some constant C, and improvement of ... over the trivial upper bound which is asymptotic to ... Our lower bound is ..., and improvement of ... over the trivial lower bound which is asymptotic to ...</dim:field>
   <dim:field mdschema="dc" element="description" qualifier="statementofresponsibility" lang="en_US">by Jason Matthew Burns.</dim:field>
   <dim:field mdschema="dc" element="description" qualifier="degree" lang="en_US">Ph.D.</dim:field>
   <dim:field mdschema="dc" element="format" qualifier="extent" lang="en_US">62 leaves</dim:field>
   <dim:field mdschema="dc" element="language" qualifier="iso" lang="en_US">eng</dim:field>
   <dim:field mdschema="dc" element="publisher" lang="en_US">Massachusetts Institute of Technology</dim:field>
   <dim:field mdschema="dc" element="rights" lang="en_US">M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.</dim:field>
   <dim:field mdschema="dc" element="rights" qualifier="uri">http://dspace.mit.edu/handle/1721.1/7582</dim:field>
   <dim:field mdschema="dc" element="subject" lang="en_US">Mathematics.</dim:field>
   <dim:field mdschema="dc" element="title" lang="en_US">The number of degree sequences of graphs</dim:field>
   <dim:field mdschema="dc" element="type" lang="en_US">Thesis</dim:field>
   <dim:field mdschema="dc" element="format" qualifier="mimetype">application/pdf</dim:field>
   <dim:field mdschema="dspace" element="authorsordered">false</dim:field>
   <dim:field mdschema="dspace" element="entity" qualifier="type">Publication</dim:field>
   <dim:field mdschema="others" element="access-status">unknown</dim:field>
   <dim:field mdschema="others" element="access-status">unknown</dim:field>
   <dim:field mdschema="cerif" element="openaire" authority="" confidence="-1">&lt;Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="ee6943c3-e852-491b-acdf-5b34a081fd1a">
	&lt;Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843&lt;/Type>
	&lt;Language>eng&lt;/Language>
   	&lt;Title>The number of degree sequences of graphs&lt;/Title>
   	&lt;PublishedIn>
    	&lt;Publication>
      	&lt;/Publication>
   	&lt;/PublishedIn>
   	&lt;PublicationDate>2007&lt;/PublicationDate>
   	&lt;Authors>
      	&lt;Author>
        	&lt;DisplayName>Burns, Jason Matthew&lt;/DisplayName>
         	&lt;Affiliation>
         		&lt;OrgUnit>
         		&lt;/OrgUnit>
         	&lt;/Affiliation>
      	&lt;/Author>
	&lt;/Authors>
   	&lt;Editors>
	&lt;/Editors>
    &lt;Publishers>
        &lt;Publisher>
            &lt;DisplayName>Massachusetts Institute of Technology&lt;/DisplayName>
            &lt;OrgUnit />
        &lt;/Publisher>
    &lt;/Publishers>
    &lt;License>http://dspace.mit.edu/handle/1721.1/7582&lt;/License>
    &lt;Keyword>Mathematics.&lt;/Keyword>
   	&lt;Abstract>We give nontrivial upper and lower bounds for the total number of distinct degree sequences among all simple, unlabeled graphs on n vertices (graphical partitions on n vertices). Our upper bound is ... for some constant C, and improvement of ... over the trivial upper bound which is asymptotic to ... Our lower bound is ..., and improvement of ... over the trivial lower bound which is asymptotic to ...&lt;/Abstract>
	&lt;Access xmlns="http://purl.org/coar/access_right" 
    >
    &lt;/Access>
&lt;/Publication>
</dim:field>
</dim:dim>
</metadata></record></GetRecord></OAI-PMH>