On a Uniqueness Problem in Discrete Tomography

Let A be a subset of the integer lattice Zn contained inside a sphere S in Rn. Suppose that for each u ∈ S we know the number of points of A visible from u. Does this information determine the set A uniquely? In this note we answer this question affirmatively, provided the center of the sphere is no...

Full description

Saved in:
Bibliographic Details
Published in:The American mathematical monthly 2024-05, Vol.131 (5), p.440-444
Main Authors: Sun, Golden, Yaskin, Vladyslav
Format: Article
Language:English
Subjects:
Discrete element method
Integer programming
Mathematical functions
Mathematical problems
Tomography
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c229t-f2885246b17710859c6dc5a372a1f6c4295b9f5bc78f217acbcf9fc5ff12467d3
container_end_page 444
container_issue 5
container_start_page 440
container_title The American mathematical monthly
container_volume 131
creator Sun, Golden
Yaskin, Vladyslav
description Let A be a subset of the integer lattice Zn contained inside a sphere S in Rn. Suppose that for each u ∈ S we know the number of points of A visible from u. Does this information determine the set A uniquely? In this note we answer this question affirmatively, provided the center of the sphere is not a rational point.
doi_str_mv 10.1080/00029890.2024.2311446
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3048956034</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3048956034</sourcerecordid><originalsourceid>FETCH-LOGICAL-c229t-f2885246b17710859c6dc5a372a1f6c4295b9f5bc78f217acbcf9fc5ff12467d3</originalsourceid><addsrcrecordid>eNo1kE1LAzEQhoMouFZ_grDgedfJJNkkR6lahUI9tOeQTRPd0v0waQ_99-7SehoGnnfm5SHkkUJJQcEzAKBWGkoE5CUySjmvrkhGNYMCtMRrkk1MMUG35C6l3biC4JiRctXlNt90ze_Rdz6l_Cv29d63edPlr01y0R98vu7b_jva4ed0T26C3Sf_cJkzsnl_W88_iuVq8Tl_WRYOUR-KgEoJ5FVNpRwrCu2qrROWSbQ0VI6jFrUOonZSBaTSutoFHZwIgY4puWUz8nS-O8R-bJYOZtcfYze-NAy40qICxkdKnCkX-5SiD2aITWvjyVAwkxrzr8ZMasxFDfsDU3BUmQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3048956034</pqid></control><display><type>article</type><title>On a Uniqueness Problem in Discrete Tomography</title><source>Taylor and Francis Science and Technology Collection</source><creator>Sun, Golden ; Yaskin, Vladyslav</creator><creatorcontrib>Sun, Golden ; Yaskin, Vladyslav</creatorcontrib><description>Let A be a subset of the integer lattice Zn contained inside a sphere S in Rn. Suppose that for each u ∈ S we know the number of points of A visible from u. Does this information determine the set A uniquely? In this note we answer this question affirmatively, provided the center of the sphere is not a rational point.</description><identifier>ISSN: 0002-9890</identifier><identifier>EISSN: 1930-0972</identifier><identifier>DOI: 10.1080/00029890.2024.2311446</identifier><language>eng</language><publisher>Washington: Taylor &amp; Francis Ltd</publisher><subject>Discrete element method ; Integer programming ; Mathematical functions ; Mathematical problems ; Tomography</subject><ispartof>The American mathematical monthly, 2024-05, Vol.131 (5), p.440-444</ispartof><rights>Copyright Taylor &amp; Francis Ltd. May 2024</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c229t-f2885246b17710859c6dc5a372a1f6c4295b9f5bc78f217acbcf9fc5ff12467d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids></links><search><creatorcontrib>Sun, Golden</creatorcontrib><creatorcontrib>Yaskin, Vladyslav</creatorcontrib><title>On a Uniqueness Problem in Discrete Tomography</title><title>The American mathematical monthly</title><description>Let A be a subset of the integer lattice Zn contained inside a sphere S in Rn. Suppose that for each u ∈ S we know the number of points of A visible from u. Does this information determine the set A uniquely? In this note we answer this question affirmatively, provided the center of the sphere is not a rational point.</description><subject>Discrete element method</subject><subject>Integer programming</subject><subject>Mathematical functions</subject><subject>Mathematical problems</subject><subject>Tomography</subject><issn>0002-9890</issn><issn>1930-0972</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNo1kE1LAzEQhoMouFZ_grDgedfJJNkkR6lahUI9tOeQTRPd0v0waQ_99-7SehoGnnfm5SHkkUJJQcEzAKBWGkoE5CUySjmvrkhGNYMCtMRrkk1MMUG35C6l3biC4JiRctXlNt90ze_Rdz6l_Cv29d63edPlr01y0R98vu7b_jva4ed0T26C3Sf_cJkzsnl_W88_iuVq8Tl_WRYOUR-KgEoJ5FVNpRwrCu2qrROWSbQ0VI6jFrUOonZSBaTSutoFHZwIgY4puWUz8nS-O8R-bJYOZtcfYze-NAy40qICxkdKnCkX-5SiD2aITWvjyVAwkxrzr8ZMasxFDfsDU3BUmQ</recordid><startdate>20240527</startdate><enddate>20240527</enddate><creator>Sun, Golden</creator><creator>Yaskin, Vladyslav</creator><general>Taylor &amp; Francis Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20240527</creationdate><title>On a Uniqueness Problem in Discrete Tomography</title><author>Sun, Golden ; Yaskin, Vladyslav</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c229t-f2885246b17710859c6dc5a372a1f6c4295b9f5bc78f217acbcf9fc5ff12467d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Discrete element method</topic><topic>Integer programming</topic><topic>Mathematical functions</topic><topic>Mathematical problems</topic><topic>Tomography</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sun, Golden</creatorcontrib><creatorcontrib>Yaskin, Vladyslav</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>The American mathematical monthly</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sun, Golden</au><au>Yaskin, Vladyslav</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On a Uniqueness Problem in Discrete Tomography</atitle><jtitle>The American mathematical monthly</jtitle><date>2024-05-27</date><risdate>2024</risdate><volume>131</volume><issue>5</issue><spage>440</spage><epage>444</epage><pages>440-444</pages><issn>0002-9890</issn><eissn>1930-0972</eissn><abstract>Let A be a subset of the integer lattice Zn contained inside a sphere S in Rn. Suppose that for each u ∈ S we know the number of points of A visible from u. Does this information determine the set A uniquely? In this note we answer this question affirmatively, provided the center of the sphere is not a rational point.</abstract><cop>Washington</cop><pub>Taylor &amp; Francis Ltd</pub><doi>10.1080/00029890.2024.2311446</doi><tpages>5</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0002-9890
ispartof The American mathematical monthly, 2024-05, Vol.131 (5), p.440-444
issn 0002-9890
1930-0972
language eng
recordid cdi_proquest_journals_3048956034
source Taylor and Francis Science and Technology Collection
subjects Discrete element method
Integer programming
Mathematical functions
Mathematical problems
Tomography
title On a Uniqueness Problem in Discrete Tomography
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-26T08%3A49%3A50IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20a%20Uniqueness%20Problem%20in%20Discrete%20Tomography&rft.jtitle=The%20American%20mathematical%20monthly&rft.au=Sun,%20Golden&rft.date=2024-05-27&rft.volume=131&rft.issue=5&rft.spage=440&rft.epage=444&rft.pages=440-444&rft.issn=0002-9890&rft.eissn=1930-0972&rft_id=info:doi/10.1080/00029890.2024.2311446&rft_dat=%3Cproquest_cross%3E3048956034%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c229t-f2885246b17710859c6dc5a372a1f6c4295b9f5bc78f217acbcf9fc5ff12467d3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=3048956034&rft_id=info:pmid/&rfr_iscdi=true