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We classify the symplectic automorphism groups for cubic fourfolds. The main inputs are the global Torelli theorem for cubic fourfolds and the classification of the fixed-point sublattices of the Leech lattice. Among the highlights of our…
In this paper, we introduce CDL, a software library designed for the analysis of permutations and linear orders subject to various structural restrictions. Prominent examples of these restrictions include pattern avoidance, a topic of…
We consider the enumeration of pattern-avoiding involutions, focusing in particular on sets defined by avoiding a single pattern of length 4. As we demonstrate, the numerical data for these problems demonstrates some surprising behavior.…
We analyze the optimal size of a congress in a representative democracy. We take an epistemic view where voters decide on a binary issue with one ground truth outcome, and each voter votes correctly according to their competence levels in…
Eleven Ultra-Compact Dwarf (UCD) and 39 extended star cluster candidates are found to be associated with the galaxy NGC 1132. This giant elliptical galaxy is the remnant of a fossil group. UCD and extended star cluster candidates are…
Recent chromosome conformation capture experiments have led to the discovery of dense, contiguous, megabase-sized topological domains that are similar across cell types and conserved across species. These domains are strongly correlated…
We show that an order in a quartic field has fewer than $3000$ essentially different generators as a $\mathbb Z$-algebra (and fewer than $200$ if the discriminant of the order is sufficiently large). This significantly improves the…
In this paper, the author introduces the concept and basic properties of finite (commutative) hyperfields. Also, the author shows that, up to isomorphism, there are exactly 2 hyperfields of order 2; 5 hyperfields of order 3; 7 hyperfields…
We consider coordinate descent (CD) methods with exact line search on convex quadratic problems. Our main focus is to study the performance of the CD method that use random permutations in each epoch and compare it to the performance of the…
Size-Change Termination (SCT) is a method of proving program termination based on the impossibility of infinite descent. To this end we use a program abstraction in which transitions are described by Monotonicity Constraints over (abstract)…
Teichm\"uller's classical mapping problem for plane domains concerns finding a lower bound for the maximal dilatation of a quasiconformal homeomorphism which holds the boundary pointwise fixed, maps the domain onto itself, and maps a given…
We prove that $\det A\leq 6^\frac{n}{6}$ whenever $A\in\{0,1\}^{n\times n}$ contains at most $2n$ ones. We also prove an upper bound on the determinant of matrices with the $k$-consecutive ones property, a generalisation of the consecutive…
We classify all cubic systems possessing the maximum number of invariant straight lines (real or complex) taking into account their multiplicities. We prove that there are exactly 23 topological different classes of such systems. For every…
Erd\H{o}s and Moser raised the question of determining the maximum number of maximal cliques or equivalently, the maximum number of maximal independent sets in a graph on $n$ vertices. Since then there has been a lot of research along these…
We present a homogeneous catalog of 275 large (effective radius $\gtrsim$ 5.3 arcsec) ultra-diffuse galaxy (UDG) candidates lying within an $\approx$ 290 square degree region surrounding the Coma cluster. The catalog results from our…
Let $d, n \in \mathbb{Z}^+$ such that $1\leq d \leq n$. A $d$-code $\mathcal{C} \subset \mathbb{F}_q^{n \times n}$ is a subset of order $n$ square matrices with the property that for all pairs of distinct elements in $\mathcal{C}$, the rank…
In the present work we present a general framework which guarantees the existence of optimal domains for isoperimetric problems within the class of $C^{1,1}$-regular domains satisfying a uniform ball condition as long as the desired…
We establish the capacity region for a class of discrete memoryless cognitive interference channel (DM-CIC) called cognitive-more-capable channel, and we show that superposition coding is the optimal encoding technique. This is the largest…
We report on a database of field extensions of the rationals, its properties and the methods used to compute it. At the moment the database encompasses roughly 100,000 polynomials generating distinct number fields over the rationals, of…
Cross-domain sentiment analysis (CDSA) helps to address the problem of data scarcity in scenarios where labelled data for a domain (known as the target domain) is unavailable or insufficient. However, the decision to choose a domain (known…