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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2512.23006 |
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| _version_ | 1866913072166207488 |
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| author | Benedetti, Carolina |
| author_facet | Benedetti, Carolina |
| contents | In this manuscript we study the subdivisions of the permutahedron $Π_n$ into two subpolytopes corresponding to flags of positroids, which are in particular flags of lattice path matroids (LPFMs). A subpolytope $P_{[u,v]}$ of $Π_n$ is a Bruhat Interval Polytope (BIP) if $P_{[u,v]}$ is the convex hull of all the permutations (viewed as points in $\RR^n$) in the interval $[u,v]$ in the Bruhat order of $§_n$. We show that the coarsest subdivisions we obtain into LPFMs are the only subdivisions of $Π_n$ via hyperplane splits, into subpolytopes corresponding to BIPs. More specifically, we describe the hyperplanes whose intersection with $Π_n$ give rise to BIPs. Hence, these subdivisions are polytopes coming from points in the complete nonnegative flag variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23006 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On subdivisions of the permutahedron and flags of lattice path matroids Benedetti, Carolina Combinatorics 52B40, 14M15 In this manuscript we study the subdivisions of the permutahedron $Π_n$ into two subpolytopes corresponding to flags of positroids, which are in particular flags of lattice path matroids (LPFMs). A subpolytope $P_{[u,v]}$ of $Π_n$ is a Bruhat Interval Polytope (BIP) if $P_{[u,v]}$ is the convex hull of all the permutations (viewed as points in $\RR^n$) in the interval $[u,v]$ in the Bruhat order of $§_n$. We show that the coarsest subdivisions we obtain into LPFMs are the only subdivisions of $Π_n$ via hyperplane splits, into subpolytopes corresponding to BIPs. More specifically, we describe the hyperplanes whose intersection with $Π_n$ give rise to BIPs. Hence, these subdivisions are polytopes coming from points in the complete nonnegative flag variety. |
| title | On subdivisions of the permutahedron and flags of lattice path matroids |
| topic | Combinatorics 52B40, 14M15 |
| url | https://arxiv.org/abs/2512.23006 |