Theory, Algorithms, Optimization & Algebra

• Here is a list of Proofs/Ideas/Posts/Musings:
  • Proof 1: Symmetric Difference over Sets form a Group
  • Proof 2: Either a Graph or its Complement are Bipartite, but not both (Assuming |V(G)| > 4)
  • Proof 3: Divisibility Rule of 3: An Integer is disvisible by 3, iff, the sum of its digits is divisible by 3
  • Post 1: Introduction to Circuit Complexity
  • Post 2: Group Automorphisms and the Graph Isomorphism problem
  • Post 3: A (very) short introduction to Cyclic Groups
  • Post 4: Counting k-Juntas, Asymptotic Influences and Hamming Geometry
  • Musing 1: First-Player Advantage in a simple Two-Player probability game

• Here is a list of notes on varied topics:
  • Notes 1: Graph Theory 1: Notes on Euler & Hamiltnoian Cycles, and their relevance to Genome Assembly
  • Notes 2: Graph Theory 2: Notes on Trees, Matchings in Bipartite Graphs and Planar Graphs

• Here is a list of technical reports/survery papers:
  • Technical Report 1: Cryptography & Group Theory
  • Technical Report 2: Unitary t-designs
  • Technical Report 3: Duality between Brascamp-Lieb Inequality & Subadditivity of Entropy
  • Technical Report 4: Efficient Algorithms for detecting & classifying credit in Graphs
  • Technical Report 5: Strengthening the Quantum Data Processing Inequality