ℤ2-Graded Number Theory

Let ℋ be the set of pairs of integers, together with addition and multiplication as given in (1) and (2) below. The arithmetics of ℋ reflects a certain arithmetics of characters of symmetric groups, whose corresponding Young diagrams are supported on hooks. This arithmetics gives rise to a ℤ 2 -grad...

Full description

Saved in:
Bibliographic Details
Published in:Communications in algebra 2006-08, Vol.34 (8), p.3077-3095
Main Authors: Hadas, Ofer, Henke, Anne, Regev, Amitai
Format: Article
Language:English
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page 3095
container_issue 8
container_start_page 3077
container_title Communications in algebra
container_volume 34
creator Hadas, Ofer
Henke, Anne
Regev, Amitai
description Let ℋ be the set of pairs of integers, together with addition and multiplication as given in (1) and (2) below. The arithmetics of ℋ reflects a certain arithmetics of characters of symmetric groups, whose corresponding Young diagrams are supported on hooks. This arithmetics gives rise to a ℤ 2 -graded (or super or hyperbolic) number theory. Many theorems from number theory have their ℤ 2 -graded analogues in ℋ. Here we study a few basic aspects of that theory.
doi_str_mv 10.1080/00927870600640086
format article
fullrecord <record><control><sourceid>informaworld</sourceid><recordid>TN_cdi_informaworld_taylorfrancis_310_1080_00927870600640086</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>163987</sourcerecordid><originalsourceid>FETCH-LOGICAL-i171t-33075b9d8c10109f2e941d01ab1663516a504b4b1ad2e983869dd4552458ee8d3</originalsourceid><addsrcrecordid>eNqFkM9KAzEYxENRcK0-QG99gej3JfnyB7xI0VooeqnnJWmyuGXbheyK9u6j-GQ-iVv01kNPc5j5DcwwNkG4QbBwC-CEsQY0gFYAVo9YgSQFVyjojBUHnw8BccEuu24DgGSsKNjk5-tb8Hn2McXp8_s2pDxdvaU276_YeeWbLl3_65i9Pj6sZk98-TJfzO6XvEaDPZcSDAUX7RoBwVUiOYUR0AfUWhJqT6CCCujjYFlptYtREQlFNiUb5ZiZv956V7V56z_a3MSy9_umzVX2u3XdlUfryv6zH8i7k6REKA8HHVfIX3RrVbM</addsrcrecordid><sourcetype>Enrichment Source</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>ℤ2-Graded Number Theory</title><source>Taylor and Francis Science and Technology Collection</source><creator>Hadas, Ofer ; Henke, Anne ; Regev, Amitai</creator><creatorcontrib>Hadas, Ofer ; Henke, Anne ; Regev, Amitai</creatorcontrib><description>Let ℋ be the set of pairs of integers, together with addition and multiplication as given in (1) and (2) below. The arithmetics of ℋ reflects a certain arithmetics of characters of symmetric groups, whose corresponding Young diagrams are supported on hooks. This arithmetics gives rise to a ℤ 2 -graded (or super or hyperbolic) number theory. Many theorems from number theory have their ℤ 2 -graded analogues in ℋ. Here we study a few basic aspects of that theory.</description><identifier>ISSN: 0092-7872</identifier><identifier>EISSN: 1532-4125</identifier><identifier>DOI: 10.1080/00927870600640086</identifier><language>eng</language><publisher>Taylor &amp; Francis Group</publisher><ispartof>Communications in algebra, 2006-08, Vol.34 (8), p.3077-3095</ispartof><rights>Copyright Taylor &amp; Francis Group, LLC 2006</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Hadas, Ofer</creatorcontrib><creatorcontrib>Henke, Anne</creatorcontrib><creatorcontrib>Regev, Amitai</creatorcontrib><title>ℤ2-Graded Number Theory</title><title>Communications in algebra</title><description>Let ℋ be the set of pairs of integers, together with addition and multiplication as given in (1) and (2) below. The arithmetics of ℋ reflects a certain arithmetics of characters of symmetric groups, whose corresponding Young diagrams are supported on hooks. This arithmetics gives rise to a ℤ 2 -graded (or super or hyperbolic) number theory. Many theorems from number theory have their ℤ 2 -graded analogues in ℋ. Here we study a few basic aspects of that theory.</description><issn>0092-7872</issn><issn>1532-4125</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNqFkM9KAzEYxENRcK0-QG99gej3JfnyB7xI0VooeqnnJWmyuGXbheyK9u6j-GQ-iVv01kNPc5j5DcwwNkG4QbBwC-CEsQY0gFYAVo9YgSQFVyjojBUHnw8BccEuu24DgGSsKNjk5-tb8Hn2McXp8_s2pDxdvaU276_YeeWbLl3_65i9Pj6sZk98-TJfzO6XvEaDPZcSDAUX7RoBwVUiOYUR0AfUWhJqT6CCCujjYFlptYtREQlFNiUb5ZiZv956V7V56z_a3MSy9_umzVX2u3XdlUfryv6zH8i7k6REKA8HHVfIX3RrVbM</recordid><startdate>20060801</startdate><enddate>20060801</enddate><creator>Hadas, Ofer</creator><creator>Henke, Anne</creator><creator>Regev, Amitai</creator><general>Taylor &amp; Francis Group</general><scope/></search><sort><creationdate>20060801</creationdate><title>ℤ2-Graded Number Theory</title><author>Hadas, Ofer ; Henke, Anne ; Regev, Amitai</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-i171t-33075b9d8c10109f2e941d01ab1663516a504b4b1ad2e983869dd4552458ee8d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hadas, Ofer</creatorcontrib><creatorcontrib>Henke, Anne</creatorcontrib><creatorcontrib>Regev, Amitai</creatorcontrib><jtitle>Communications in algebra</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hadas, Ofer</au><au>Henke, Anne</au><au>Regev, Amitai</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>ℤ2-Graded Number Theory</atitle><jtitle>Communications in algebra</jtitle><date>2006-08-01</date><risdate>2006</risdate><volume>34</volume><issue>8</issue><spage>3077</spage><epage>3095</epage><pages>3077-3095</pages><issn>0092-7872</issn><eissn>1532-4125</eissn><abstract>Let ℋ be the set of pairs of integers, together with addition and multiplication as given in (1) and (2) below. The arithmetics of ℋ reflects a certain arithmetics of characters of symmetric groups, whose corresponding Young diagrams are supported on hooks. This arithmetics gives rise to a ℤ 2 -graded (or super or hyperbolic) number theory. Many theorems from number theory have their ℤ 2 -graded analogues in ℋ. Here we study a few basic aspects of that theory.</abstract><pub>Taylor &amp; Francis Group</pub><doi>10.1080/00927870600640086</doi><tpages>19</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0092-7872
ispartof Communications in algebra, 2006-08, Vol.34 (8), p.3077-3095
issn 0092-7872
1532-4125
language eng
recordid cdi_informaworld_taylorfrancis_310_1080_00927870600640086
source Taylor and Francis Science and Technology Collection
title ℤ2-Graded Number Theory
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-13T06%3A39%3A38IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-informaworld&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=%E2%84%A42-Graded%20Number%20Theory&rft.jtitle=Communications%20in%20algebra&rft.au=Hadas,%20Ofer&rft.date=2006-08-01&rft.volume=34&rft.issue=8&rft.spage=3077&rft.epage=3095&rft.pages=3077-3095&rft.issn=0092-7872&rft.eissn=1532-4125&rft_id=info:doi/10.1080/00927870600640086&rft_dat=%3Cinformaworld%3E163987%3C/informaworld%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-i171t-33075b9d8c10109f2e941d01ab1663516a504b4b1ad2e983869dd4552458ee8d3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true