Related papers: Splittings of link concordance groups
We study the restrictions, the strict fixed points, and the strict quotients of the partition complex $|\Pi_n|$, which is the $\Sigma_n$-space attached to the poset of proper nontrivial partitions of the set $\{1,\ldots,n\}$. We express the…
The bipolar filtration introduced by T. Cochran, S. Harvey, and P. Horn is a framework for the study of smooth concordance of topologically slice knots and links. It is known that there are topologically slice 1-bipolar knots which are not…
The discrepancy of a point set quantifies how well the points are distributed, with low-discrepancy point sets demonstrating exceptional uniform distribution properties. Such sets are integral to quasi-Monte Carlo methods, which approximate…
Let $F \hookrightarrow X \to B$ be a fibre bundle with structure group $G$, where $B$ is $(d{-}1)$-connected and of finite dimension, $d \geq 1$. We prove that the strong L-S category of $X$ is less than or equal to $m + \frac{\dim B}{d}$,…
Denote by $\mathrm m(S)$ the multiplicity of a numerical semigroup $S$. A covariety is a nonempty family $\mathscr{C}$ of numerical semigroups that fulfills the following conditions: there is the minimum of $\mathscr{C},$ the intersection…
Tied links and the tied braid monoid were introduced recently by the authors and used to define new invariants for classical links. Here, we give a version purely algebraic-combinatoric of tied links. With this new version we prove that the…
Recent developments of high-order CCM have been to extend existing formalism and codes to $s \ge \frac 12$ for both the ground and excited states, and independently to "generalised" expectation values for a wide range of one- and two-body…
This paper establishes connections between the structure of a semigroup and the minimum spans of distance labellings of its Cayley graphs. We show that certain general restrictions on the minimum spans are equivalent to the semigroup being…
The main aim of this work is to introduce and justify the study of semi-covarities. A {\it semi-covariety} is a non-empty family $\mathcal{F}$ of numerical semigroups such that it is closed under finite intersections, has a minimum,…
Let $S$ be a finite non-commutative semigroup. The commuting graph of $S$, denoted $\cg(S)$, is the graph whose vertices are the non-central elements of $S$ and whose edges are the sets $\{a,b\}$ of vertices such that $a\ne b$ and $ab=ba$.…
For an integer $\ell\geqslant 2$, the $\ell$-component connectivity of a graph $G$, denoted by $\kappa_{\ell}(G)$, is the minimum number of vertices whose removal from $G$ results in a disconnected graph with at least $\ell$ components or a…
The Cartesian tree of a sequence captures the relative order of the sequence's elements. In recent years, Cartesian tree matching has attracted considerable attention, particularly due to its applications in time series analysis. Consider a…
The semiclassical approximation for the partition function in Chern-Simons gauge theory is derived using the invariant integration method. Volume and scale factors which were undetermined and had to be fixed by hand in previous derivations…
In this paper, we start by showing that the intertwining relationship between two minimal Markov semigroups acting on Hilbert spaces implies that any recurrent extensions, in the sense of It\^o, of these semigroups satisfy the same…
We study symplectic minimal resolutions of weighted projective planes $\mathbb{CP}(a,b,c)$ from the perspective of disconnected symplectic divisors with symplectic log Kodaira dimension $-\infty$. Building on the techniques developed in our…
Let $G$ be a linear algebraic group acting linearly on a $G$-variety $\mathcal{V}$, and let $k[\mathcal{V}]^G$ be the corresponding algebra of invariant polynomial functions. A separating set $S \subseteq k[\mathcal{V}]^G$ is a set of…
The Lloyd Theorem of (Sol\'e, 1989) is combined with the Schwartz-Zippel Lemma of theoretical computer science to derive non-existence results for perfect codes in the Lee metric, NRT metric, mixed Hamming metric, and for the sum-rank…
The problem of source algebra equivalences between blocks at the ends of the maximal strings of spin blocks of the symmetric and alternating groups has recently been settled, but so far there has not even been a candidate of the tilting…
We show that if a finite point set $P\subseteq \mathbb{R}^2$ has the fewest congruence classes of triangles possible, up to a constant $M$, then at least one of the following holds. (1) There is a $\sigma>0$ and a line $l$ which contains…
The general structure of the perturbative expansion of the vacuum expectation value of a product of Wilson-loop operators is analyzed in the context of Chern-Simons gauge theory. Wilson loops are opened into Wilson lines in order to unravel…