We consider permutations sortable by $k$ passes through a deterministic pop stack. We show that for any $k\in\mathbb{N}$ the set is characterised by finitely many patterns, answering a question of Claesson and Guðmundsson. Moreover, these sets of patterns are algorithmically constructible.
Our characterisation demands a more precise definition than in previous literature of what it means for a permutation to avoid a set of barred and unbarred patterns. We propose a new notion called $2$-avoidance.
We prove that the set of permutations sorted by a stack of depth t ≥ 3 and an infinite stack in series has infinite basis, by constructing an infinite antichain. This answers an open question on identifying the point at which, in a sorting process with two stacks in series, the basis changes from finite to infinite.
Writing analytics has emerged as a sub-field of learning analytics, with applications including the provision of formative feedback to students in developing their writing capacities. Rhetorical markers in writing have become a key feature in this feedback, with a number of tools being developed across research and teaching contexts. However, there is no shared corpus of texts annotated by these tools, nor is it clear how the tool annotations compare. Thus, resources are scarce for comparing tools for both tool development and pedagogic purposes. In this paper, we conduct such a comparison and introduce a sample corpus of texts representative of the particular genres, a subset of which has been annotated using three rhetorical analysis tools (one of which has two versions). This paper aims to provide both a description of the tools and a shared dataset in order to support extensions of existing analyses and tool design in support of writing skill development. We intend the description of these tools, which share a focus on rhetorical structures, alongside the corpus, to be a preliminary step to enable further research, with regard to both tool development and tool interaction
We consider permutations sortable by k passes through a deterministic pop stack. We show that for any k ∈ N the set is characterised by finitely many patterns, answering a question of Claesson and Guðmundsson.Our characterisation demands a more precise definition than in previous literature of what it means for a permutation to avoid a set of barred and unbarred patterns. We propose a new notion called 2-avoidance.
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