Related papers: Flip-sort and combinatorial aspects of pop-stack s…
Consider a permutation p to be any finite list of distinct positive integers. A statistic is a function St whose domain is all permutations. Let S(p,q) be the set of shuffles of two disjoint permutations p and q. We say that St is shuffle…
An $F$-zip over a scheme $S$ over a finite field is a certain object of semi-linear algebra consisting of a locally free module with a descending filtration and an ascending filtration and a $\Frob_q$-twisted isomorphism between the…
This paper deals with lattice congruences of the weak order on the symmetric group, and initiates the investigation of the cover graphs of the corresponding lattice quotients. These graphs also arise as the skeleta of the so-called…
The emerging field of Diverse Intelligence seeks to identify, formalize, and understand commonalities in behavioral competencies across a wide range of implementations. Especially interesting are simple systems that provide unexpected…
The paper "Sorting with Bialgebras and Distributive Laws" by Hinze et al. uses the framework of bialgebraic semantics to define sorting algorithms. From distributive laws between functors they construct pairs of sorting algorithms using…
We initiate the study of subpolytopes of the permutahedron that arise as the convex hulls of stack-sorting on permutations. We primarily focus on $Ln1$ permutations, i.e., permutations of length $n$ whose penultimate and last entries are…
Generalizing stack sorting and $c$-sorting for permutations, we define the permutree sorting algorithm. Given two disjoint subsets $U$ and $D$ of $\{2, \dots, n-1\}$, the $(U,D)$-permutree sorting tries to sort the permutation $\pi \in…
Several sequences of free cumulants that count binary plane trees correspond to sequences of classical cumulants that count the decreasing versions of the same trees. Using two new operations on colored binary plane trees that we call…
In this paper we examine sorting on the assumption that we do not know in advance which way to sort a sequence of numbers and we set at work simple local comparison and swap operators whose repeating application ends up in sorted sequences.…
We introduce and analyse a new, extremely simple, randomised sorting algorithm: - choose a pair of indices $\{i, j\}$ according to some distribution $q$; - sort the elements in positions $i$ and $j$ of the array in ascending order. Choosing…
Much of the copious literature on the subject of sorting has concentrated on minimizing the number of comparisons and/or exchanges/copies. However, a more appropriate yardstick for the performance of sorting algorithms is based on the total…
The in-order traversal provides a natural correspondence between binary trees with a decreasing vertex labeling and endofunctions on a finite set. By suitably restricting the vertex labeling we arrive at a class of trees that we call…
We study a family of sorting match puzzles on grids, which we call permutation match puzzles. In this puzzle, each row and column of a $n \times n$ grid is labeled with an ordering constraint -- ascending (A) or descending (D) -- and the…
Picat, a new member of the logic programming family, follows a different doctrine than Prolog in offering the core logic programming concepts: arrays and maps as built-in data types; implicit pattern matching with explicit unification and…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Sorting is a fundamental operation in various applications and a traditional research topic in computer science. Improving the performance of sorting operations can have a significant impact on many application domains. For high-performance…
The study of sorting permutations by block interchanges has recently been stimulated by a phenomenon observed in the genome maintenance of certain ciliate species. The result was the identification of a block interchange operation that…
Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard average-case analysis is ammenable to this method. Here we…
In this paper, we propose a useful replacement for quicksort-style utility functions. The replacement is called Symmetry Partition Sort, which has essentially the same principle as Proportion Extend Sort. The maximal difference between them…
We consider the simultaneous movement of finitely many colored points in space, calling it a spatial sorting process. The name suggests a purpose that drives the collection to a configuration of increased or decreased order. Mapping such a…