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- W2999159987 abstract "Hasebe and Tsujie characterized the set of induced N-free and bowtie-free posets as a certain class of recursively defined subposets which they term “$mathcal {V}$-posets”. Here we offer a new characterization of $mathcal {V}$-posets by introducing a property we refer to as autonomy. A poset $mathcal {P}$ is said to be autonomous if there exists a directed acyclic graph D (with adjacency matrix U) whose transitive closure is $mathcal {P}$, with the property that any total ordering of the vertices of D so that Gaussian elimination of UTU proceeds without row swaps is a linear extension of $mathcal {P}$. Autonomous posets arise from the theory of pressing sequences in graphs, a problem with origins in computational evolutionary biology. The pressing sequences of a graph can be partitioned into families corresponding to posets; because of the interest in enumerating pressing sequences, we investigate when this partition has only one block, that is, when the pressing sequences are all linear extensions of a single autonomous poset. We also provide an efficient algorithm for recognition of autonomy using structural information and the forbidden subposet characterization, and we discuss a few open questions that arise in connection with these posets." @default.
- W2999159987 created "2020-01-23" @default.
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- W2999159987 date "2019-11-22" @default.
- W2999159987 modified "2023-09-29" @default.
- W2999159987 title "A New Characterization of $mathcal {V}$-Posets" @default.
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- W2999159987 doi "https://doi.org/10.1007/s11083-019-09510-6" @default.
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