Explicit Construction of Ramanujan Bigraphs

  • Cristina Ballantine
  • Brooke Feigon
  • Radhika Ganapathy
  • Janne Kool
  • Kathrin Maurischat
  • Amy Wooding
Part of the Association for Women in Mathematics Series book series (AWMS, volume 2)


We construct explicitly an infinite family of Ramanujan graphs which are bipartite and biregular. Our construction starts with the Bruhat–Tits building of an inner form of \(\mathrm{SU}_{3}(\mathbb{Q}_{p})\). To make the graphs finite, we take successive quotients by infinitely many discrete co-compact subgroups of decreasing size.

MSC 2010:

11E39 11E57 16W10 



The authors would like to thank Dan Ciubotaru, Judith Ludwig, and Rachel Newton for helpful discussions. This work was initiated at the CIRM workshop, “Femmes en nombre” in October 2013 and the authors would like to thank CIRM, Microsoft Research, the National Science Foundation DMS-1303457, the Clay Mathematics Institute, and the Number Theory Foundation for supporting the workshop.This work was partially supported by a grant from the Simons Foundation (#245997 to Cristina Ballantine).This work was partially supported by grants from the National Science Foundation (DMS-1201446) and from PSC-CUNY (Brooke Feigon).This work was partially supported by the European Social Fund (Kathrin Maurischat).


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Cristina Ballantine
    • 1
  • Brooke Feigon
    • 2
  • Radhika Ganapathy
    • 3
  • Janne Kool
    • 4
  • Kathrin Maurischat
    • 5
  • Amy Wooding
    • 6
  1. 1.Department of Mathematics and Computer ScienceCollege of the Holy CrossWorcesterUSA
  2. 2.Department of MathematicsThe City College of New YorkNew YorkUSA
  3. 3.Department of MathematicsThe University of British ColumbiaVancouverCanada
  4. 4.Max Planck Institute for MathematicsBonnGermany
  5. 5.Mathematisches InstitutUniversität HeidelbergHeidelbergGermany
  6. 6.The Department of Mathematics and StatisticsMcGill UniversityMontrealCanada

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