Type-B generalized triangulations and determinantal ideals
| dc.creator | Soll, Daniel | |
| dc.creator | Welker, Volkmar | |
| dc.date | 2006-07-06 | |
| dc.date.accessioned | 2026-07-07T07:18:06Z | |
| dc.date.available | 2026-07-07T07:18:06Z | |
| dc.description | For $n\geq 3$, let $Ω_n$ be the set of line segments between the vertices of a convex $n$-gon. For $j\geq 2$, a $j$-crossing is a set of $j$ line segments pairwise intersecting in the relative interior of the $n$-gon. We identify line-segments in $Ω_{2n}$ which can be transformed into each other by a $180^\circ$-rotation of the $2n$-gon. Let $\F_n$ be the set $Ω_{2n}$ after identification, then the complex $\D_{n,k}$ of type-B generalized triangulations is the simplicial complex of subsets of $\F_n$ not containing any $(k+1)$-crossing in the above sense. We demonstrate that $\D_{n,k}$ is a pure, $k(n-k)-1+kn$ dimensional complex that decomposes into a $kn-1$-simplex and a $k(n-k)-1$ dimensional homology sphere. We give a term-order on the monomials in the variables $X_{ij}, 1\leq i,j\leq n$, such that the corresponding initial ideal of the determinantal ideal generated by the $(k+1)$ times $(k+1)$ minors of the generic $n \times n$ matrix contains the Stanley-Reisner ideal of $\D_{n,k}$. We show that the minors form a Gröbner-Basis whenever $k\in\{1,n-2,n-1\}$. We conjecture this result to be true for all values of $k<n$. | |
| dc.identifier | https://arxiv.org/abs/math/0607159 | |
| dc.identifier | http://arxiv.org/abs/math/0607159 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114179 | |
| dc.subject | Combinatorics | |
| dc.subject | Commutative Algebra | |
| dc.subject | 05e99, 13p10, 52b12 | |
| dc.title | Type-B generalized triangulations and determinantal ideals | |
| dc.type | text |