Explicit Construction of Ramanujan Bigraphs

  • Cristina Ballantine
  • Brooke Feigon
  • Radhika Ganapathy
  • Janne Kool
  • Kathrin Maurischat
  • Amy Wooding
Conference paper

DOI: 10.1007/978-3-319-17987-2_1

Part of the Association for Women in Mathematics Series book series (AWMS, volume 2)
Cite this paper as:
Ballantine C., Feigon B., Ganapathy R., Kool J., Maurischat K., Wooding A. (2015) Explicit Construction of Ramanujan Bigraphs. In: Bertin M., Bucur A., Feigon B., Schneps L. (eds) Women in Numbers Europe. Association for Women in Mathematics Series, vol 2. Springer, Cham

Abstract

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 

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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