{"id":"https://openalex.org/W7225328476","doi":"https://doi.org/10.5281/zenodo.23989840","title":"Block-Wise Construction of Tetramagic Squares of Orders 48(2304), 52(2704), 56(3136), 60(3600) and 64(4096)","display_name":"Block-Wise Construction of Tetramagic Squares of Orders 48(2304), 52(2704), 56(3136), 60(3600) and 64(4096)","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225328476","doi":"https://doi.org/10.5281/zenodo.23989840"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23989840","doi":"https://doi.org/10.5281/zenodo.23989840","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23989840","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23989840","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109991551","display_name":"Inder Jeet Taneja","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4104125","display_name":"Universidade Federal de Santa Catarina","ror":"https://ror.org/041akq887","country_code":"BR","type":"education","lineage":["https://openalex.org/I4104125"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Inder J. Taneja","raw_affiliation_strings":["Formerly, Professor of Mathematics, Federal University of Santa Catarina, Florian\u00f3polis, SC, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Formerly, Professor of Mathematics, Federal University of Santa Catarina, Florian\u00f3polis, SC, Brazil","institution_ids":["https://openalex.org/I4104125"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109991551"],"corresponding_institution_ids":["https://openalex.org/I4104125"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.7817000150680542,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.7817000150680542,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.0210999995470047,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.02019999921321869,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/compound-constructions","display_name":"compound constructions","score":0.7409999966621399},{"id":"https://openalex.org/keywords/power-sums","display_name":"sums of powers","score":0.4309999942779541}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7412999868392944},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6466000080108643},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6452999711036682},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4747999906539917},{"id":"https://openalex.org/C2983050975","wikidata":"https://www.wikidata.org/wiki/Q88287214","display_name":"Block structure","level":3,"score":0.40149998664855957},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.3959999978542328},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3885999917984009},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3691999912261963},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3682999908924103},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.3515999913215637},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.32269999384880066},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3149999976158142},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.25949999690055847},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23989840","doi":"https://doi.org/10.5281/zenodo.23989840","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23989840","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23989841","doi":"https://doi.org/10.5281/zenodo.23989841","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23989841","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23989840","doi":"https://doi.org/10.5281/zenodo.23989840","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23989840","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225306024","https://openalex.org/W7225330014","https://openalex.org/W7124555072","https://openalex.org/W4288602424","https://openalex.org/W7225335246","https://openalex.org/W3209693610","https://openalex.org/W4394877714","https://openalex.org/W7225232237","https://openalex.org/W4310338146","https://openalex.org/W4313449351"],"abstract_inverted_index":{"The":[0,20,101],"ordinary":[1],"compound":[2],"construction":[3],"is":[4,36,103],"applied":[5],"to":[6],"five":[7],"retained":[8,99],"normal":[9,22],"tetramagic":[10,23,40],"seeds":[11],"of":[12,42,69,88,109,116],"orders":[13,26],"48,":[14],"52,":[15],"56,":[16],"60":[17],"and":[18,31,61,65,82,106],"64.":[19],"resulting":[21],"squares":[24],"have":[25],"2304,":[27],"2704,":[28],"3136,":[29],"3600":[30],"4096,":[32],"respectively.":[33],"Each":[34],"output":[35],"partitioned":[37],"into":[38],"translated":[39],"blocks":[41],"the":[43,66,70,79,83,93,98],"corresponding":[44],"seed":[45],"order.":[46],"We":[47],"give":[48],"a":[49,104],"complete":[50,80,117],"proof":[51],"covering":[52],"normality,":[53],"all":[54],"four":[55],"power":[56],"conditions":[57],"on":[58],"rows,":[59],"columns":[60],"both":[62],"principal":[63],"diagonals,":[64],"pairwise":[67],"distinction":[68],"block":[71,84],"constants":[72,81],"for":[73],"each":[74],"power.":[75],"Explicit":[76],"formulas":[77],"describe":[78],"constants.":[85],"Mathematical":[86],"consequences":[87],"iteration":[89],"are":[90,119],"distinguished":[91],"from":[92],"finite":[94],"calculations":[95],"documented":[96],"in":[97],"record.":[100],"contribution":[102],"specialization":[105],"computational":[107],"documentation":[108],"an":[110],"established":[111],"product":[112],"construction.":[113],"Text":[114],"files":[115],"work":[118],"attached.":[120]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-11-06T00:00:00"}
