Geodesic
Pure \(\mathcal{O}\)-sequences arising from \(2\)-dimensional PS ear-decomposable simplicial complexes
Steven Klee1 ; Brian Nugent1
1Seattle University
The electronic journal of combinatorics, Tome 27 (2020) no. 3
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We show that the $h$-vector of a $2$-dimensional PS ear-decomposable simplicial complex is a pure $\mathcal{O}$-sequence. This provides a strengthening of Stanley's conjecture for matroid $h$-vectors in rank $3$. Our approach modifies the approach of combinatorial shifting for arbitrary simplicial complexes to the setting of $2$-dimensional PS ear-decomposable complexes, which allows us to greedily construct pure multicomplex corresponding to each PS ear-decomposable complex.
DOI : 10.37236/8389
Classification : 05E45, 05B35, 52B40
Mots-clés : Stanley's conjecture, 2-dimensional simplicial complexes

Steven Klee  1   ; Brian Nugent  1

1 Seattle University 
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     author = {Steven Klee and Brian Nugent},
     title = {Pure {\(\mathcal{O}\)-sequences} arising from \(2\)-dimensional {PS} ear-decomposable simplicial complexes},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {3},
     doi = {10.37236/8389},
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Steven Klee; Brian Nugent. Pure \(\mathcal{O}\)-sequences arising from \(2\)-dimensional PS ear-decomposable simplicial complexes. The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/8389

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