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Jakob Zimmermann

Publications and source records attributed to Jakob Zimmermann.

9 recordsLinked to original sources
arXiv2026

Faster, Higher, Stronger? The Impact of GenAI on Knowledge Work Productivity - Evidence from the Field

The rise of generative artificial intelligence (GenAI) has fueled high expectations regarding its potential to enhance knowledge work productivity in terms of efficiency and quality. Building on task-technology fit (TTF) theory, we empirically examine the extent of GenAI's productivity effect for different task types. We conducted a randomized lab-in-the-field experiment with 128 knowledge workers from a multinational industrial organization. Participants completed three representative knowledge work tasks (knowledge acquisition, packaging, and creation), either with or without GenAI. Results show that GenAI consistently increases efficiency across tasks. However, its impact on quality is task-contingent: quality increases for knowledge packaging and creation but declines for knowledge acquisition. Furthermore, GenAI tends to reduce quality variance for knowledge packaging and creation, primarily benefiting lower-performing knowledge workers. However, it increases quality variance for knowledge acquisition. These findings contribute to a more granular, differentiated understanding of GenAI's productivity impact and hold implications for research and practice alike.

cs.HC↗
arXiv2024

Induced Turán problem in bipartite graphs

The classical extremal function for a graph $H$, $ex(K_n, H)$ is the largest number of edges in a subgraph of $K_n$ that contains no subgraph isomorphic to $H$. Note that defining $ex(K_n, H-ind)$ by forbidding induced subgraphs isomorphic to $H$ is not very meaningful for a non-complete $H$ since one can avoid it by considering a clique. For graphs $F$ and $H$, let $ex(K_n, \{F, H-ind\})$ be the largest number of edges in an $n$-vertex graph that contains no subgraph isomorphic to $F$ and no induced subgraph isomorphic to $H$. Determining this function asymptotically reduces to finding either $ex(K_n, F)$ or $ex(K_n, H)$, unless $H$ is a biclique or both $F$ and $H$ are bipartite. Here, we consider the bipartite setting, $ex(K_{n,n}, \{F, H-ind\})$ when $K_n$ is replaced with $K_{n,n}$, $F$ is a biclique, and $H$ is a bipartite graph. Our main result, a strengthening of a result by Sudakov and Tomon, implies that for any $d\geq 2$ and any $K_{d,d}$-free bipartite graph $H$ with each vertex in one part of degree either at most $d$ or a full degree, so that there are at most $d-2$ full degree vertices in that part, one has $ex(K_{n,n}, \{K_{t,t}, H-ind\}) = o(n^{2-1/d})$. This provides an upper bound on the induced Turán number for a wide class of bipartite graphs and implies in particular an extremal result for bipartite graphs of bounded VC-dimension by Janzer and Pohoata.

math.CO↗
arXiv2019

Existence of symmetric maximal noncrossing collections of $k$-element sets

We investigate the existence of maximal collections of mutually noncrossing $k$-element subsets of $\left\{ 1, \dots, n \right\}$ that are invariant under adding $k\pmod n$ to all indices. Our main result is that such a collection exists if and only if $k$ is congruent to $0, 1$ or $-1$ modulo $n/\operatorname{GCD}(k,n)$. Moreover, we present some algebraic consequences of our result related to self-injective Jacobian algebras.

math.CO↗
arXiv2018

Extreme representations of semirings

This is a write-up of the discussions during the meetings of the study group on representation theory of semirings which was organized at the Department of Mathematics, Uppsala University, during the academic year 2017-2018. The main emphasis is on classification of various classes of "irreducible" representations for various concrete semirings.

math.RT↗
arXiv2018

Simple transitive $2$-representations of left cell $2$-subcategories of projective functors for star algebras

In this paper we study simple transitive $2$-representations of certain $2$-subcategories of the $2$-category of projective functors over a star algebra. We show that in the simplest case, which is associated to the Dynkin type $A_2$, simple transitive $2$-representations are classified by cell $2$-representations. In the general case we conjecture that there exist many simple transitive $2$-representations which are not cell $2$-representations and provide some evidence for our conjecture.

math.RT↗
arXiv2017

Counting Quasi-Idempotent Irreducible Integral Matrices

Given any polynomial $p$ in $C[X]$, we show that the set of irreducible matrices satisfying $p(A)=0$ is finite. In the specific case $p(X)=X^2-nX$, we count the number of irreducible matrices in this set and analyze the arising sequences and their asymptotics. Such matrices turn out to be related to generalized compositions and generalized partitions.

math.CO↗
arXiv2017

Simple transitive 2-representations of small quotients of Soergel bimodules

In all finite Coxeter types but $I_2(12)$, $I_2(18)$ and $I_2(30)$, we classify simple transitive $2$-rep\-re\-sen\-ta\-ti\-ons for the quotient of the $2$-category of Soergel bimodules over the coinvariant algebra which is associated to the two-sided cell that is the closest one to the two-sided cell containing the identity element. It turns out that, in most of the cases, simple transitive $2$-representations are exhausted by cell $2$-representations. However, in Coxeter types $I_2(2k)$, where $k\geq 3$, there exist simple transitive $2$-representations which are not equivalent to cell $2$-representations.

math.RT↗
arXiv2016

Simple transitive $2$-representations of Soergel bimodules in type $B_2$

We prove that every simple transitive $2$-representation of the fiat $2$-category of Soergel bimodules (over the coinvariant algebra) in type $B_2$ is equivalent to a cell $2$-representation. We also describe some general properties of the $2$-category of Soergel bimodules for arbitrary finite Dihedral groups.

math.RT↗