Generalized polymorphisms
We find all functions $f_0,f_1,\dots,f_m\colon \{0,1\}^n \to \{0,1\}$ and $g_0,g_1,\dots,g_n\colon \{0,1\}^m \to \{0,1\}$ satisfying the following identity for all $n \times m$ matrices $(z_{ij}) \in \{0,1\}^{n \times m}$: \[ f_0(g_1(z_{11},\dots,z_{1m}),\dots,g_n(z_{n1},\dots,z_{nm})) = g_0(f_1(z_{...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Chase, Gilad Filmus, Yuval |
| description | We find all functions $f_0,f_1,\dots,f_m\colon \{0,1\}^n \to \{0,1\}$ and
$g_0,g_1,\dots,g_n\colon \{0,1\}^m \to \{0,1\}$ satisfying the following
identity for all $n \times m$ matrices $(z_{ij}) \in \{0,1\}^{n \times m}$: \[
f_0(g_1(z_{11},\dots,z_{1m}),\dots,g_n(z_{n1},\dots,z_{nm})) =
g_0(f_1(z_{11},\dots,z_{n1}),\dots,f_m(z_{1m},\dots,z_{nm})). \] Our results
generalize work of Dokow and Holzman (2010), which considered the case $g_0 =
g_1 = \cdots = g_n$, and of Chase, Filmus, Minzer, Mossel and Saurabh (2022),
which considered the case $g_0 \neq g_1 = \cdots = g_n$. |
| doi_str_mv | 10.48550/arxiv.2305.10073 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2305_10073</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2305_10073</sourcerecordid><originalsourceid>FETCH-LOGICAL-a673-b743705bb6d890df6cbfd79d11d329f8c23cf3514c654e9efc0390fbbbbac7053</originalsourceid><addsrcrecordid>eNotzr0OgjAUBeAuDkZ9ACd9AfCW21I6GqJoYuLiTvobSUBISYz49CJ6ljOdk4-QNYWYZZzDToVX9YwTBB5TAIFzsi7cwwVVV29nt11bD00bunvVN_2SzLyqe7f694Lcjodbfoou1-Kc7y-RSgVGWjAUwLVObSbB-tRob4W0lFpMpM9MgsYjp8yknDnpvAGU4PUYZcYhLsjmdzvZyi5UjQpD-TWWkxE_OLg2fQ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Generalized polymorphisms</title><source>arXiv.org</source><creator>Chase, Gilad ; Filmus, Yuval</creator><creatorcontrib>Chase, Gilad ; Filmus, Yuval</creatorcontrib><description>We find all functions $f_0,f_1,\dots,f_m\colon \{0,1\}^n \to \{0,1\}$ and
$g_0,g_1,\dots,g_n\colon \{0,1\}^m \to \{0,1\}$ satisfying the following
identity for all $n \times m$ matrices $(z_{ij}) \in \{0,1\}^{n \times m}$: \[
f_0(g_1(z_{11},\dots,z_{1m}),\dots,g_n(z_{n1},\dots,z_{nm})) =
g_0(f_1(z_{11},\dots,z_{n1}),\dots,f_m(z_{1m},\dots,z_{nm})). \] Our results
generalize work of Dokow and Holzman (2010), which considered the case $g_0 =
g_1 = \cdots = g_n$, and of Chase, Filmus, Minzer, Mossel and Saurabh (2022),
which considered the case $g_0 \neq g_1 = \cdots = g_n$.</description><identifier>DOI: 10.48550/arxiv.2305.10073</identifier><language>eng</language><subject>Computer Science - Computer Science and Game Theory ; Computer Science - Discrete Mathematics ; Mathematics - Combinatorics</subject><creationdate>2023-05</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2305.10073$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2305.10073$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Chase, Gilad</creatorcontrib><creatorcontrib>Filmus, Yuval</creatorcontrib><title>Generalized polymorphisms</title><description>We find all functions $f_0,f_1,\dots,f_m\colon \{0,1\}^n \to \{0,1\}$ and
$g_0,g_1,\dots,g_n\colon \{0,1\}^m \to \{0,1\}$ satisfying the following
identity for all $n \times m$ matrices $(z_{ij}) \in \{0,1\}^{n \times m}$: \[
f_0(g_1(z_{11},\dots,z_{1m}),\dots,g_n(z_{n1},\dots,z_{nm})) =
g_0(f_1(z_{11},\dots,z_{n1}),\dots,f_m(z_{1m},\dots,z_{nm})). \] Our results
generalize work of Dokow and Holzman (2010), which considered the case $g_0 =
g_1 = \cdots = g_n$, and of Chase, Filmus, Minzer, Mossel and Saurabh (2022),
which considered the case $g_0 \neq g_1 = \cdots = g_n$.</description><subject>Computer Science - Computer Science and Game Theory</subject><subject>Computer Science - Discrete Mathematics</subject><subject>Mathematics - Combinatorics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzr0OgjAUBeAuDkZ9ACd9AfCW21I6GqJoYuLiTvobSUBISYz49CJ6ljOdk4-QNYWYZZzDToVX9YwTBB5TAIFzsi7cwwVVV29nt11bD00bunvVN_2SzLyqe7f694Lcjodbfoou1-Kc7y-RSgVGWjAUwLVObSbB-tRob4W0lFpMpM9MgsYjp8yknDnpvAGU4PUYZcYhLsjmdzvZyi5UjQpD-TWWkxE_OLg2fQ</recordid><startdate>20230517</startdate><enddate>20230517</enddate><creator>Chase, Gilad</creator><creator>Filmus, Yuval</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230517</creationdate><title>Generalized polymorphisms</title><author>Chase, Gilad ; Filmus, Yuval</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a673-b743705bb6d890df6cbfd79d11d329f8c23cf3514c654e9efc0390fbbbbac7053</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Computer Science - Computer Science and Game Theory</topic><topic>Computer Science - Discrete Mathematics</topic><topic>Mathematics - Combinatorics</topic><toplevel>online_resources</toplevel><creatorcontrib>Chase, Gilad</creatorcontrib><creatorcontrib>Filmus, Yuval</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Chase, Gilad</au><au>Filmus, Yuval</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Generalized polymorphisms</atitle><date>2023-05-17</date><risdate>2023</risdate><abstract>We find all functions $f_0,f_1,\dots,f_m\colon \{0,1\}^n \to \{0,1\}$ and
$g_0,g_1,\dots,g_n\colon \{0,1\}^m \to \{0,1\}$ satisfying the following
identity for all $n \times m$ matrices $(z_{ij}) \in \{0,1\}^{n \times m}$: \[
f_0(g_1(z_{11},\dots,z_{1m}),\dots,g_n(z_{n1},\dots,z_{nm})) =
g_0(f_1(z_{11},\dots,z_{n1}),\dots,f_m(z_{1m},\dots,z_{nm})). \] Our results
generalize work of Dokow and Holzman (2010), which considered the case $g_0 =
g_1 = \cdots = g_n$, and of Chase, Filmus, Minzer, Mossel and Saurabh (2022),
which considered the case $g_0 \neq g_1 = \cdots = g_n$.</abstract><doi>10.48550/arxiv.2305.10073</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.2305.10073 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_2305_10073 |
| source | arXiv.org |
| subjects | Computer Science - Computer Science and Game Theory Computer Science - Discrete Mathematics Mathematics - Combinatorics |
| title | Generalized polymorphisms |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-06T22%3A41%3A10IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Generalized%20polymorphisms&rft.au=Chase,%20Gilad&rft.date=2023-05-17&rft_id=info:doi/10.48550/arxiv.2305.10073&rft_dat=%3Carxiv_GOX%3E2305_10073%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |