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Looking for a New Version of Gordon’s Identities


We give a commutative algebra viewpoint on Andrews recursive formula for the partitions appearing in Gordon’s identities, which are a generalization of Rogers–Ramanujan identities. Using this approach and differential ideals, we conjecture a family of partition identities which extend Gordon’s identities. This family is indexed by \(r\ge 2.\) We prove the conjecture for \(r=2\) and \(r=3.\)

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I would like to express my deep gratitude to Hussein Mourtada, my Ph.D advisor, for suggesting me this project and for his constant help. I am very thankful to Bernard Teissier for his help and his corrections of the earlier version of this paper. I also would like to thank Jehanne Dousse and Frédéric Jouhet for showing interest in this work and for giving me the opportunity to talk about it in their seminar. I also would like to thank the two anonymous reviewers for their useful suggestions and comments.

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Correspondence to Pooneh Afsharijoo.

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Afsharijoo, P. Looking for a New Version of Gordon’s Identities. Ann. Comb. 25, 543–571 (2021).

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  • Gordon’s identities
  • Space of arcs
  • Hilbert series

Mathematics Subject Classification

  • 05A17
  • 12H05
  • 13D40
  • 13P10