Related papers: More results on stack-sorting for set partitions

In the paper [J. Combin. Theory Ser. A 43 (1986), 103--113], Stanley gives formulas for the number of plane partitions in each of ten symmetry classes. This paper together with results by Andrews [J. Combin. Theory Ser. A 66 (1994), 28-39]…

This paper concerns arithmetic families of $\varphi$-modules over reduced affinoid spaces. For such a family, we first prove that the slope polygons is lower semicontinuous around any rigid point. If the slope polygons are locally constant…

The order and chain polytopes, introduced by Richard P. Stanley, form a pair of Ehrhart equivalent polytopes associated to a given finite poset. A conjecture by Takayuki Hibi and Nan Li states that the $f$-vector of the chain polytope…

We initiate a study of the streaming complexity of constraint satisfaction problems (CSPs) when the constraints arrive in a random order. We show that there exists a CSP, namely $\textsf{Max-DICUT}$, for which random ordering makes a…

This article extends a paper of Abraham and Bonnet which generalised the famous Hausdorff characterisation of the class of scattered linear orders. Abraham and Bonnet gave a poset hierarchy that characterised the class of scattered posets…

Despite the recent progress in genome sequencing and assembly, many of the currently available assembled genomes come in a draft form. Such draft genomes consist of a large number of genomic fragments (scaffolds), whose order and/or…

We define a family of maps on lattice paths, called sweep maps, that assign levels to each step in the path and sort steps according to their level. Surprisingly, although sweep maps act by sorting, they appear to be bijective in general.…

Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…

A set partition avoids a pattern if no subdivision of that partition standardizes to the pattern. There exists a bijection between set partitions and restricted growth functions (RGFs) on which Wachs and White defined four statistics of…

When solving the Hamiltonian path problem it seems natural to be given additional precedence constraints for the order in which the vertices are visited. For example one could decide whether a Hamiltonian path exists for a fixed starting…

In this paper, we introduce and formalize a rank-one partitioning learning paradigm that unifies partitioning methods that proceed by summarizing a data set using a single vector that is further used to derive the final clustering…

Birkhoff's representation theorem (Birkhoff, 1937) defines a bijection between elements of a distributive lattice and the family of upper sets of an associated poset. Although not used explicitly, this result is at the backbone of the…

The pop-stack-sorting process is a variation of the stack-sort process. We consider a deterministic version of this process, and provide a new lower bound of $\frac{3}{5}n$ for the number of sorts to fully sort a uniformly randomly chosen…

We introduce a new algorithm for the structural analysis of finite abstract simplicial complexes based on local homology. Through an iterative and top-down procedure, our algorithm computes a stratification $\pi$ of the poset $P$ of…

We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and…

We give a framework to produce constructible functions from natural functors between categories, without need of a morphism of moduli spaces to model the functor. We show using the Riemann-Hilbert correspondence that any natural (derived)…

In the online sorting problem, we have an array $A$ of $n$ cells, and receive a stream of $n$ items $x_1,\dots,x_n\in [0,1]$. When an item arrives, we need to immediately and irrevocably place it into an empty cell. The goal is to minimize…

Given a finite group $G$, we denote by $\psi\,'(G)$ the product of element orders of $G$. Our main result proves that the restriction of $\psi\,'$ to abelian $p$-groups of order $p^n$ is strictly increasing with respect to a natural order…

Motivated by efforts to incorporate sheaves into networking, we seek to reinterpret pathfinding algorithms in terms of cellular sheaves, using Dijkstra's algorithm as an example. We construct sheaves on a graph with distinguished source and…

This is the third installment in a series of papers on algebraic set theory. In it, we develop a uniform approach to sheaf models of constructive set theories based on ideas from categorical logic. The key notion is that of a "predicative…