Related papers: Clones above the unary clone
We show that a plane continuum X is indecomposable iff X has a sequence (U_n) of not necessarily distinct complementary domains satisfying what we call the double-pass condition: If one draws an open arc A_n in each U_n whose ends limit…
Algebras on the natural numbers and their clones of term operations can be classified according to their descriptive complexity. We give an example of a closed algebra which has only unary operations and whose clone of term operations is…
Given three positive integers $n,a,b$ with $n=ab$, we determine the base size of the symmetric group and of the alternating group of degree $n$ in their action on the set of partitions into $b$ parts having cardinality $a$.
Assuming the existence of $\mathfrak c$ incomparable selective ultrafilters, we classify the non-torsion Abelian groups of cardinality $\mathfrak c$ that admit a countably compact group topology. We show that for each $\kappa \in [\mathfrak…
We construct a theory of holant clones to capture the notion of expressibility in the holant framework. Their role is analogous to the role played by functional clones in the study of weighted counting Constraint Satisfaction Problems. We…
This paper continues the study of combinatorial properties of binary functions --- that is, functions $f:2^E\rightarrow\mathbb{C}$ such that $f(\emptyset)=1$, where $E$ is a finite set. Binary functions have previously been shown to admit…
For each $N$ an infinite number of Conformal Field Theories is presented that has the same fusion rules as SO(N) level 2. These new theories are obtained as extensions of the chiral algebra of $SO(NM^2)$ level 2, and correspond to new…
The trade-offs among various output fidelities of asymmetric universal cloning machines are investigated. First we find out all the attainable optimal output fidelities for the 1 to 3 asymmetric universal cloning machine and it turns out…
We use mathematical induction to prove that the horizontal composition in the class of coherently diagonal complexes is indeed a binary operation. That is to say, the embedding of two coherently diagonal complexes in an alternating planar…
A commutative algebra over a field gives rise to a representation of the category of finite sets and surjective maps. We consider the restriction of this representation to the subcategory of sets of cardinality at most $r$. For each $r$, we…
We introduce and study operadic categories with cardinalities in finite sets and establish conditions under which their associated theories of operads and algebras are equivalent to the standard framework introduced in 2015 by Batanin and…
A partition is finitary if all its blocks are finite. For a cardinal $\mathfrak{a}$ and a natural number $n$, let $\mathrm{fin}(\mathfrak{a})$ and $\mathscr{B}_{n}(\mathfrak{a})$ be the cardinalities of the set of finite subsets and the set…
We propose a partitioning of the set of unlabelled, connected cubic graphs into two disjoint subsets named genes and descendants, where the cardinality of the descendants is much larger than that of the genes. The key distinction between…
We present an order-theoretic approach to the study of countably infinite locally 2-arc-transitive bipartite graphs. Our approach is motivated by techniques developed by Warren and others during the study of cycle-free partial orders. We…
We prove the existence of common hypercyclic entire functions for uncountable families of translation type operators. Contrary to our previous work [34], here the parameter which reflects the uncountable family lies on the unit circle. On…
We show that there is some absolute constant $c>0$, such that for any union-closed family $\mathcal{F} \subseteq 2^{[n]}$, if \mbox{$|\mathcal{F}| \geq (\frac{1}{2}-c)2^n$}, then there is some element $i \in [n]$ that appears in at least…
Some techniques for the use of bitwise operations are described in the article. As an example, an open problem of isomorphism-free generations of combinatorial objects is discussed. An equivalence relation on the set of square binary…
We classify the countable ultrahomogeneous 2-vertex-colored graphs in which the color classes are imprimitive, i.e., up to complementation they form disjoint unions of cliques. This generalizes work by Jenkinson, Lockett and Truss as well…
An algebraic structure with two constants and one ternary operation, which is not completely commutative, is put forward to accommodate ternary Boolean algebras. When the ternary operation is interpreted as Church's conditioned disjunction,…
It is known that a countable $\omega$-categorical structure interprets all finite structures primitively positively if and only if its polymorphism clone maps to the clone of projections on a two-element set via a continuous clone…