The greedy basis equals the theta basis: A rank two haiku

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• 作者：Man Wai Cheung^a ; ^{mwc31@cam.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Mark Gross^b ; ^{mg475@dpmms.cam.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Greg Muller^c ; ^{morilac@umich.edu" class="auth_mail" title="E-mail the corresponding author} ; Gregg Musiker^d ; ^{musiker@math.umn.edu" class="auth_mail" title="E-mail the corresponding author} ; Dylan Rupel^e ; ^{drupel@nd.edu" class="auth_mail" title="E-mail the corresponding author} ; Salvatore Stella^f ; ^{stella@mat.uniroma1.it" class="auth_mail" title="E-mail the corresponding author} ; Harold Williams^g ; ^{hwilliams@math.utexas.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Cluster algebras ; Greedy basis ; Theta functions ; Scattering diagrams ; Broken lines
• 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：150-171
• 全文大小：510 K

文摘

We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee–Li–Zelevinsky and the theta basis of Gross–Hacking–Keel–Kontsevich.