On homomorphisms from the Hamming cube to \(\mathbb{Z}\)

DOI10.1007/BF02783426zbMath1040.05021arXiv1206.3152OpenAlexW2063177160MaRDI QIDQ1425648

David Galvin

Publication date: 17 March 2004

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.3152

zbMATH Keywords

probabilityBoolean latticecomplete graph3-colourings

Mathematics Subject Classification ID

Combinatorial probability (60C05) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Boolean functions (06E30)

Related Items (19)

The diameter of a random subgraph of the hypercube ⋮ Note on the number of balanced independent sets in the Hamming cube ⋮ Rigidity of 3-colorings of the discrete torus ⋮ Random mappings of scaled graphs. ⋮ The number of 4-colorings of the Hamming cube ⋮ The number of maximal independent sets in the Hamming cube ⋮ Homomorphisms from the torus ⋮ Rigidity of proper colorings of \(\mathbb{Z}^d \) ⋮ Independent sets in the middle two layers of Boolean lattice ⋮ Independent sets in the hypercube revisited ⋮ Wasserstein distance to independence models ⋮ Delocalization of uniform graph homomorphisms from \({\mathbb{Z}}^2\) to \({\mathbb{Z}} \) ⋮ Markov random fields, Markov cocycles and the 3-colored chessboard ⋮ The Growth Constant of Odd Cutsets in High Dimensions ⋮ \(H\)-coloring tori ⋮ A Threshold Phenomenon for Random Independent Sets in the Discrete Hypercube ⋮ On the distribution of range for tree-indexed random walks ⋮ Lipschitz Functions on Expanders are Typically Flat ⋮ Logarithmic variance for the height function of square-ice

Cites Work

• Odd and even Hamming spheres also have minimum boundary
• On the ratio of optimal integral and fractional covers
• Generalized rank functions and an entropy argument
• On random graph homomorphisms into \({\mathbb{Z}}\)
• Matchings and covers in hypergraphs
• Two combinatorial covering theorems
• Range of cube-indexed random walk
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