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We give the first construction of explicit constant-degree lossless vertex expanders.
Arithmetic of quaternions
Leonard E Dickson · 1922
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On the arithmetic of quaternions
Gordon Pall · 1940
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An inequality related to the isoperimetric inequality
LH Loomis and H Whitney · 1949
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Ramanujan graphs
Alexander Lubotzky, Ralph Phillips, and Peter Sarnak · 1988
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Self-routing superconcentrators
Nicholas Pippenger · 1993
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Random Cayley graphs and expanders
Noga Alon and Yuval Roichman · 1994
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Discrete groups, expanding graphs and invariant measures
Alex Lubotzky · 1994
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Existence and explicit constructions of q + 1 q+1 regular Ramanujan graphs for every prime power q q
Moshe Morgenstern · 1994
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Linear time erasure codes with nearly optimal recovery
N. Alon, J. Edmonds, and M. Luby · 1995
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Eigenvalues and expansion of regular graphs
Nabil Kahale · 1995
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On-Line Algorithms for Path Selection in a Nonblocking Network
Sanjeev Arora, FT Leighton, and Bruce M Maggs · 1996
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Expander codes
Michael Sipser and Daniel Spielman · 1996
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Optimal construction of edge-disjoint paths in random graphs
Andrei Z Broder, Alan M Frieze, Stephen Suen, and Eli Upfal · 1998
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The Ramanujan property for regular cubical complexes
Bruce W Jordan and Ron Livné · 2000
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Explicit unique-neighbor expanders
Noga Alon and Michael Capalbo · 2002
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Randomness conductors and constant-degree lossless expanders
Michael Capalbo, Omer Reingold, Salil Vadhan, and Avi Wigderson · 2002
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On quaternions and octonions
John H Conway and Derek A Smith · 2003
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Explicit constructions of Ramanujan complexes of type A ~ d \tilde{A}_{d}
Alexander Lubotzky, Beth Samuels, and Uzi Vishne · 2005
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Ramanujan complexes of type A ~ d \tilde{A}_{d}
Alexander Lubotzky, Beth Samuels, and Uzi Vishne · 2005
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Robust local testability of tensor products of LDPC codes
Irit Dinur, Madhu Sudan, and Avi Wigderson · 2006
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Expander graphs and their applications
Shlomo Hoory, Nathan Linial, and Avi Wigderson · 2006
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Monotone circuits for the majority function
Shlomo Hoory, Avner Magen, and Toniann Pitassi · 2006
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Lossless condensers, unbalanced expanders, and extractors
Amnon Ta-Shma, Christopher Umans, and David Zuckerman · 2007
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Combining geometry and combinatorics: A unified approach to sparse signal recovery
Radu Berinde, Anna C Gilbert, Piotr Indyk, Howard Karloff, and Martin J Strauss · 2008
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Unbalanced Expanders from Multiplicity Codes
Itay Kalev and Amnon Ta-Shma · 2022
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c 3 c^{3} -Locally Testable Codes from Lossless Expanders
Ting-Chun Lin and Min-Hsiu Hsieh · 2022
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Good quantum LDPC codes with linear time decoder from lossless expanders
Ting-Chun Lin and Min-Hsiu Hsieh · 2022
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Asymptotically good quantum and locally testable classical LDPC codes
Pavel Panteleev and Gleb Kalachev · 2022
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Bipartite unique-neighbour expanders via Ramanujan graphs
Ron Asherov and Irit Dinur · 2023
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HDX Condensers
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Tensor products of weakly smooth codes are robust
Eli Ben-Sasson and Michael Viderman · 2009
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Unbalanced expanders and randomness extractors from Parvaresh–Vardy codes
Venkatesan Guruswami, Christopher Umans, and Salil Vadhan · 2009
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Almost Euclidean subspaces of ℓ 1 N \ell_{1}^{N} via expander codes
Venkatesan Guruswami, James R Lee, and Alexander Razborov · 2010
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Deterministic construction of a high dimensional ℓ p \ell_{p} section in ℓ 1 n \ell_{1}^{n} for any p < 2 p<2
Zohar S Karnin · 2011
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Linear-time decoding of regular expander codes
Michael Viderman · 2013
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Explicit bounds for primes in arithmetic progressions
Michael A Bennett, Greg Martin, Kevin O’Bryant, and Andrew Rechnitzer · 2018
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Itay Cohen, Roy Roth, and Amnon Ta-Shma · 2023
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Simple Constructions of Unique Neighbor Expanders from Error-correcting Codes
Swastik Kopparty, Noga Ron-Zewi, and Shubhangi Saraf · 2023
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Quasi-Linear Size PCPs with Small Soundness from HDX
Mitali Bafna, Dor Minzer, and Nikhil Vyas · 2024
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Two-Sided Lossless Expanders in the Unbalanced Setting, 2024
Eshan Chattopadhyay, Mohit Gurumukhani, Noam Ringach, and Yunya Zhao · 2024
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Expanders and PCPs: Emergence from Local to Global
Irit Dinur · 2024
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Expansion of High-Dimensional Cubical Complexes: with Application to Quantum Locally Testable Codes
Irit Dinur, Ting-Chun Lin, and Thomas Vidick · 2024
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New explicit constant-degree lossless expanders
Louis Golowich · 2024
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Explicit two-sided unique-neighbor expanders
Jun-Ting Hsieh, Theo McKenzie, Sidhanth Mohanty, and Pedro Paredes · 2024
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Computational hardness of detecting graph lifts and certifying lift-monotone properties of random regular graphs
Dmitriy Kunisky and Xifan Yu · 2024
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Unique-neighbor Expanders with Better Expansion for Polynomial-sized Sets
Yeyuan Chen · 2025
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Explicit Two-Sided Vertex Expanders Beyond the Spectral Barrier
Jun-Ting Hsieh, Ting-Chun Lin, Sidhanth Mohanty, Ryan O’Donnell, and Rachel Yun Zhang · 2025
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Theory at the Institute and Beyond, February 2025
Nikhil Srivastava · 2025
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