Geodesic
Resolving two conjectures on staircase encodings and boundary grids of \(132\) and \(123\)-avoiding permutations
Shyam Sivasathya Narayanan1
1Harvard University
The electronic journal of combinatorics, Tome 26 (2019) no. 3
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This paper analyzes relations between pattern avoidance of certain permutations and graphs on staircase grids and boundary grids, and proves two conjectures posed by Bean, Tannock, and Ulfarsson (2015). More specifically, this paper enumerates a certain family of staircase encodings and proves that the downcore graph, a certain graph established on the boundary grid, is pure if and only if the permutation corresponding to the boundary grid avoids the classical patterns 123 and 2143.
DOI : 10.37236/8171
Classification : 05A05, 05A15
Mots-clés : graphs on staircase grids, graphs on boundary grids

Shyam Sivasathya Narayanan  1

1 Harvard University 
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     title = {Resolving two conjectures on staircase encodings and boundary grids of \(132\) and \(123\)-avoiding permutations},
     journal = {The electronic journal of combinatorics},
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Shyam Sivasathya Narayanan. Resolving two conjectures on staircase encodings and boundary grids of \(132\) and \(123\)-avoiding permutations. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8171

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