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pro vyhledávání: '"Rowlands, Rowan"'
Autor:
Bayer, Margaret, Denker, Mark, Milutinović, Marija Jelić, Rowlands, Rowan, Sundaram, Sheila, Xue, Lei
Publikováno v:
SIAM J. on Discrete Mathematics,Vol. 38 (2), 1630--1675 (2024)
We define the $k$-cut complex of a graph $G$ with vertex set $V(G)$ to be the simplicial complex whose facets are the complements of sets of size $k$ in $V(G)$ inducing disconnected subgraphs of $G$. This generalizes the Alexander dual of a graph com
Externí odkaz:
http://arxiv.org/abs/2304.13675
Autor:
Bayer, Margaret, Denker, Mark, Milutinović, Marija Jelić, Rowlands, Rowan, Sundaram, Sheila, Xue, Lei
Inspired by work of Fr\"oberg (1990), and Eagon and Reiner (1998), we define the \emph{total $k$-cut complex} of a graph $G$ to be the simplicial complex whose facets are the complements of independent sets of size $k$ in $G$. We study the homotopy t
Externí odkaz:
http://arxiv.org/abs/2209.13503
Autor:
Rowlands, Rowan
Given a polytopal complex $X$, we examine the topological complement of its $k$-skeleton. We construct a long exact sequence relating the homologies of the skeleton complements and links of faces in $X$, and using this long exact sequence, we obtain
Externí odkaz:
http://arxiv.org/abs/2209.08434
The matching complex $M(G)$ of a graph $G$ is the set of all matchings in $G$. A Buchsbaum simplicial complex is a generalization of both a homology manifold and a Cohen--Macaulay complex. We give a complete characterization of the graphs $G$ for whi
Externí odkaz:
http://arxiv.org/abs/2110.11302
Autor:
Rowlands, Rowan
Given a finite CAT(0) cubical complex, we define a flag simplicial complex associated to it, called the crossing complex. We show that the crossing complex holds much of the combinatorial information of the original cubical complex: for example, hype
Externí odkaz:
http://arxiv.org/abs/2004.12517
Autor:
Rowlands, Rowan
In 1984, Dancis proved that any $d$-dimensional simplicial manifold is determined by its $(\lfloor d/2 \rfloor + 1)$-skeleton. This paper adapts his proof to the setting of cubical complexes that can be embedded into a cube of arbitrary dimension. Un
Externí odkaz:
http://arxiv.org/abs/1906.03736
Autor:
Alper, Jarod, Rowlands, Rowan
We investigate the space of syzygies of the apolar ideals $\det_n^\perp$ and ${\rm perm}_n^\perp$ of the determinant $\det_n$ and permanent ${\rm perm}_n$ polynomials. Shafiei had proved that these ideals are generated by quadrics and provided a mini
Externí odkaz:
http://arxiv.org/abs/1709.09286
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