On derivatives of graphon parameters

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• 作者：Lá ; szló ; Mikló ; s Lová ; sz^a ; ^{lmlovasz@math.mit.edu" class="auth_mail" title="E-mail the corresponding author} ; Yufei Zhao^b ; ¹ ; ^{yufei.zhao@maths.ox.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Graphons ; Graph limits ; Graph homomorphisms ; Gâ ; teaux derivatives
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：145
• 期：Complete
• 页码：364-368
• 全文大小：243 K

文摘

We give a short elementary proof of the main theorem in the paper “Differential calculus on graphon space” by Diao et al. (2015) [2], which says that any graphon parameters whose class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0097316516300796&_mathId=si1.gif&_user=111111111&_pii=S0097316516300796&_rdoc=1&_issn=00973165&md5=1e1275e7bf07ca6964fc353d08c00a06" title="Click to view the MathML source">(N+1)class="mathContainer hidden">class="mathCode">$(N+1)$-th derivatives all vanish must be a linear combination of homomorphism densities class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0097316516300796&_mathId=si110.gif&_user=111111111&_pii=S0097316516300796&_rdoc=1&_issn=00973165&md5=3643d3983c1829a5f5ace690cfe37b30" title="Click to view the MathML source">t(H,−)class="mathContainer hidden">class="mathCode">$t(H,-)$ over graphs H on at most N edges.