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29 papers · 1 filter
An insertion algorithm for catabolizability
Jonah Blasiak
Motivated by our recent work relating canonical bases to combinatorics of Garsia-Procesi modules \cite{B}, we give an insertion algorithm that computes the catabolizability of the…
Combinatorial Polytope Enumeration
Sandeep Koranne, Anand Kulkarni
We describe a provably complete algorithm for the generation of a tight, possibly exact superset of all combinatorially distinct simple n-facet polytopes in R^d, along with their g…
Anatomy of a young giant component in the random graph
Jian Ding, Jeong Han Kim, Eyal Lubetzky +1
We provide a complete description of the giant component of the Erdős-Rényi random graph as soon as it emerges from the scaling window, i.e., for where $ε^3…
Positivity for cluster algebras from surfaces
Gregg Musiker, Ralf Schiffler, Lauren Williams
We give combinatorial formulas for the Laurent expansion of any cluster variable in any cluster algebra coming from a triangulated surface (with or without punctures), with respect…
The group of symmetries of the Tower of Hanoi graph
So Eun Park
I prove that the group of symmetries of the Tower of Hanoi graph with k pegs and n disks, denoted H_n^k, is isomorphic to the group of permutations of k elements, S_k, for all k gr…
New Proofs of the Green-Tao-Ziegler Dense Model Theorem: An Exposition
Omer Reingold, Luca Trevisan, Madhur Tulsiani +1
Green, Tao and Ziegler prove ``Dense Model Theorems'' of the following form: if R is a (possibly very sparse) pseudorandom subset of set X, and D is a dense subset of R, then D may…