On the lattice property of shard orders
Research output: Contribution to conferences › Paper › Contributed › peer-review
Contributors
Abstract
Let L be a congruence-uniform lattice. In this article, we investigate the shard order on L that was introduced by N. Reading. When L can be realized as a poset of regions of a hyperplane arrangement the shard order is always a lattice. For general L, however, this fails. We provide a necessary condition for the shard order to be a lattice, and we show how to construct a congruence-uniform lattice L0 from L such that the shard order on L0 fails to be a lattice.
Details
| Original language | English |
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| Publication status | Published - 2018 |
| Peer-reviewed | Yes |
Conference
| Title | 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 |
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| Duration | 16 - 20 July 2018 |
| City | Hanover |
| Country | United States of America |
Keywords
ASJC Scopus subject areas
Keywords
- Biclosed sets, Congruence-uniform lattices, Crosscut theorem, Interval doubling, Möbius function, Semidistributive lattices