Related papers: Modified difference ascent sequences and Fishburn …
A linking system of difference sets is a collection of mutually related group difference sets, whose advantageous properties have been used to extend classical constructions of systems of linked symmetric designs. The central problems are…
Transformer architectures, capable of capturing sequential dependencies in the history of user interactions, have become the dominant approach in sequential recommender systems. Despite their success, such models consider sequence elements…
The length $\mathsf{is}(\pi)$ of a longest increasing subsequence in a permutation $\pi$ has been extensively studied. An increasing subsequence is one that has no descents. We study generalizations of this statistic by finding longest…
Twisted diagrams are "diagrams" with components in different categories. Structure maps are defined using auxiliary data which consists of functors relating the various categories to each other. Prime examples of the construction are…
Phylogenetic tree reconstruction is traditionally based on multiple sequence alignments (MSAs) and heavily depends on the validity of this information bottleneck. With increasing sequence divergence, the quality of MSAs decays quickly.…
Tree-like tableaux are objects in bijection with alternative or permutation tableaux. They have been the subject of a fruitful combinatorial study for the past few years. In the present work, we define and study a new subclass of tree-like…
In this paper, we address the problem of change in an abstract argumentation system. We focus on a particular change: the addition of a new argument which interacts with previous arguments. We study the impact of such an addition on the…
Changing base composition during the evolution of biological sequences can mislead some of the phylogenetic inference techniques in current use. However, detecting whether such a process has occurred may be difficult, since convergent…
Sequence classification is the supervised learning task of building models that predict class labels of unseen sequences of symbols. Although accuracy is paramount, in certain scenarios interpretability is a must. Unfortunately, such…
It is known when we call a poset P, a $\mathcal{P}$-chain permutational poset, given a subset of permutations $\mathcal{P}$ of the symmetric group $S_{n}$. In this work, we use the same idea to study subsets of words of length $n$, that are…
A multiplication on persistence diagrams is introduced by means of Schubert calculus. The key observation behind this multiplication comes from the fact that the representation space of persistence modules has the structure of the Schubert…
We define twisted Frobenius extensions of graded superrings. We develop equivalent definitions in terms of bimodule isomorphisms, trace maps, bilinear forms, and dual sets of generators. The motivation for our study comes from…
We show that the way in which Betti cohomology varies in a proper family of complex algebraic varieties is controlled by certain "higher discriminants" in the base. These discriminants are defined in terms of transversality conditions,…
To perform well on unseen and potentially out-of-distribution samples, it is desirable for machine learning models to have a predictable response with respect to transformations affecting the factors of variation of the input. Here, we…
We study a sorting procedure (run-sorting) on permutations, where runs are rearranged in lexicographic order. We describe a rather surprising bijection on permutations on length $n$, with the property that it sends the set of peak-values to…
Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data…
The reconstruction of phylogenies from DNA or protein sequences is a major task of computational evolutionary biology. Common phenomena, notably variations in mutation rates across genomes and incongruences between gene lineage histories,…
Difference sets and their generalisations to difference families arise from the study of designs and many other applications. Here we give a brief survey of some of these applications, noting in particular the diverse definitions of…
We study a fixed-window counting system in which integers are represented by words of constant length while the alphabet grows as needed. This viewpoint arises from De Bruijn sequences: for fixed order $n$, the reverse prefer-max sequence…
In their paper [1] on Wilf-equivalence for singleton classes, Backelin, Xin, and West introduce a transformation $\phi^*$, defined by an iterative process and operating on (all) full rook placements on Ferrers boards. In [3],…