{"title":"Exercise Solutions","authors":"René Orth","doi":"10.1061/9780784409213.apb","DOIUrl":"https://doi.org/10.1061/9780784409213.apb","url":null,"abstract":"Linear Algebra Methods in Combinatorics This file contains solutions to some of the exercises, and it will be periodically updated. 1 Exercise Set 2 Exercise 4 (One-Distance Sets). A regular simplex is a set of n + 1 points in R n such that any two points are at distance 1. Prove that no set with this property can have more points. n are such that d(s i , s j) = 1 for all i = j (1) where d() is the Euclidean distance, then m ≤ n + 1. If you cannot prove this bound, try to prove the simpler bound m ≤ n + 2. Warm up (\" n + 2 \"). We can assume wlog that d() is the square of the Euclidean distance (this will not change the problem), that is d(x, y) = k","PeriodicalId":292995,"journal":{"name":"An Invitation to Applied Category Theory","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132394868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Logic of Behavior: Sheaves, Toposes, and Internal Languages","authors":"","doi":"10.1017/9781108668804.008","DOIUrl":"https://doi.org/10.1017/9781108668804.008","url":null,"abstract":"ly speaking, the universally-quantified predicate corresponds to the subsheaf given by the following pullback:","PeriodicalId":292995,"journal":{"name":"An Invitation to Applied Category Theory","volume":"213 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121156832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Databases: Categories, Functors, and Universal Constructions","authors":"Brendan Fong, David I. Spivak","doi":"10.1017/9781108668804.004","DOIUrl":"https://doi.org/10.1017/9781108668804.004","url":null,"abstract":"","PeriodicalId":292995,"journal":{"name":"An Invitation to Applied Category Theory","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127278391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Collaborative Design: Profunctors, Categorification, and Monoidal Categories","authors":"Brendan Fong, David I. Spivak","doi":"10.1017/9781108668804.005","DOIUrl":"https://doi.org/10.1017/9781108668804.005","url":null,"abstract":"","PeriodicalId":292995,"journal":{"name":"An Invitation to Applied Category Theory","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122983066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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