Related papers: An enumeration process for racks
We refine the complexity landscape for enumeration problems by introducing very low classes defined by using Boolean circuits as enumerators. We locate well-known enumeration problems, e.g., from graph theory, Gray code enumeration, and…
We discuss the theory of certain partially ordered sets that capture the structure of commutation classes of words in monoids. As a first application, it follows readily that counting words in commutation classes is #P-complete. We then…
Relation extraction (RE) is an indispensable information extraction task in several disciplines. RE models typically assume that named entity recognition (NER) is already performed in a previous step by another independent model. Several…
A fundamental step in the classification of finite-dimensional complex pointed Hopf algebras is the determination of all finite-dimensional Nichols algebras of braided vector spaces arising from groups. The most important class of braided…
Counting non-isomorphic tree-like multigraphs that include self-loops and multiple edges is an important problem in combinatorial enumeration, with applications in chemical graph theory, polymer science, and network modeling. Traditional…
The paper addresses the $k$-tangle enumeration problem. We introduce a notion of cascade diagram for $k$-tangle projections. An effective enumeration algorithm for projections is proposed based on cascade representation. Tangles projections…
The finite orbits of the braid group action on Stokes matrices are studied and are shown to be the orbits on ordered sets of reflections, generating finite groups. All invariants of a reflection arrangement are determined. Determination of…
We study the rank one completion problem for tensors of arbitrary orders. The notion of rank one determinable tensors is introduced. We explore its properties and propose a recursive algorithm for computing rank one tensor completion. This…
Tits has defined Steinberg groups and Kac-Moody groups for any root system and any commutative ring R. We establish a Curtis-Tits-style presentation for the Steinberg group St of any rank > 2 irreducible affine root system, for any R.…
In 2009, Ghani, Hancock and Pattinson gave a tree-like representation of stream processors $A^{\mathbb{N}} \rightarrow B^{\mathbb{N}}$. In 2021, Garner showed that this representation can be established in terms of algebraic theory and…
A rack on $[n]$ can be thought of as a set of maps $(f_x)_{x \in [n]}$, where each $f_x$ is a permutation of $[n]$ such that $f_{(x)f_y} = f_y^{-1}f_xf_y$ for all $x$ and $y$. In 2013, Blackburn showed that the number of isomorphism classes…
Codd's rule of entity integrity stipulates that every table has a primary key. Hence, the attributes of the primary key carry unique and complete value combinations. In practice, data cannot always meet such requirements. Previous work…
We design a class of Chudnovsky-type algorithms multiplying k elements of a finite extension of order n a finite field K. We prove that these algorithms give a tensor decomposition of the k-multiplication for which the rank is linear in n…
For a row-finite graph G with no sinks and in which every loop has an exit, we construct an isomorphism between Ext(C*(G)) and coker(A-I), where A is the vertex matrix of G. If c is the class in Ext(C*(G)) associated to a graph obtained by…
A fertile field of research in theoretical computer science investigates the representation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations,…
We study parabolic double cosets in a Coxeter system by decomposing them into atom(ic coset)s, a generalization of simple reflections introduced in a joint work with Elias, Libedinsky, Patimo. We define and classify braid relations between…
Many problems in operations research require that constraints be specified in the model. Determining the right constraints is a hard and laborsome task. We propose an approach to automate this process using artificial intelligence and…
Formalized $1$-category theory forms a core component of various libraries of mathematical proofs. However, more sophisticated results in fields from algebraic topology to theoretical physics, where objects have "higher structure," rely on…
We explore some connections between vectors of integers and integer partitions seen as bi-infinite words. This methodology enables us on the one hand to obtain enumerations connecting products of hook lengths and vectors of integers. This…
Inspired by the work of Amdeberhan, Can, and Moll on broken necklaces, we define a broken bracelet as a linear arrangement of marked and unmarked vertices and introduce a generalization called $n$-stars, which is a collection of $n$ broken…