Related papers: Absorption and directed J\'{o}nsson terms
Congruence modular and congruence distributive varieties can be characterized by the existence of sequences of Gumm and J\'onsson terms, respectively. Such sequences have variable lengths, in general. It is immediate from the above…
We study the validity of congruence inclusions of the form $ \alpha ( \beta \circ \alpha \gamma \circ \beta \circ \dotsc \circ \alpha \gamma \circ \beta ) \subseteq \alpha \beta \circ \alpha \gamma \circ \alpha \beta \circ \dots$ in…
We solve some problems about relative lengths of Maltsev conditions, in particular, we give an affirmative answer to a classical problem raised by A. Day more than fifty years ago. In detail, both congruence distributive and congruence…
We characterize absorption in finite idempotent algebras by means of J\'onsson absorption and cube term blockers. As an application we show that it is decidable whether a given subset is an absorbing subuniverse of an algebra given by the…
A. Mitschke showed that a variety with an $m$-ary near-unanimity term has J\'onsson terms $t_0, \dots, t _{2m-4} $ witnessing congruence distributivity. We show that Mitschke's result is sharp. We also evaluate the best possible number of…
We show that a variety with J\'onsson terms $t_1, \dots, t_{n-1}$ has directed J\'onsson terms $d_1, \dots, d_{n-1}$, for the same value of the indices, solving a problem raised by Kazda et al.. Refined results are obtained for locally…
We prove that for finite, finitely related algebras the concepts of an absorbing subuniverse and a J\'onsson absorbing subuniverse coincide. Consequently, it is decidable whether a given subset is an absorbing subuniverse of the…
Motivated by the Poisson Dixmier-Moeglin equivalence problem, a systematic study of commutative unitary rings equipped with a {\em biderivation}, namely a binary operation that is a derivation in each argument, is here begun, with an eye…
We study a class of Riemannian manifolds with respect to the covariant derivative of their curvature tensors. We introduce geometrically the class of directed Riemannian manifolds of pointwise constant relative sectional curvature and give…
In their study of a binomial sum related to Wolstenholme's theorem, Chamberland and Dilcher prove that the corresponding sequence modulo primes $p$ satisfies congruences that are analogous to Lucas' theorem for the binomial coefficients…
Let $g(x)$ be a fixed non-constant complex polynomial. It was conjectured by Schinzel that if $g(h(x))$ has boundedly many terms, then $h(x)\in \C[x]$ must also have boundedly many terms. Solving an older conjecture raised by R\'enyi and by…
In (B-Gran, 2004), was given a categorical formulation of the Shifting Lemma which is a characterization of the Congruence Modular Varieties among all the variety of Universal Algebra, introduced in (Gumm, 1983). Starting from a…
We discuss the recently developed method of refined absorption and how it is used to provide a new proof of the Existence Conjecture for combinatorial designs. This method can also be applied to resolve open problems in extremal and…
Constraint languages that arise from finite algebras have recently been the object of study, especially in connection with the Dichotomy Conjecture of Feder and Vardi. An important class of algebras are those that generate congruence…
We extend some properties of pullbacks which are known to hold in a Mal'tsev context to the more general context of Gumm categories. The varieties of universal algebras which are Gumm categories are precisely the congruence modular ones.…
We give a new, systematic proof for a recent result of Larry Guth and thus also extend the result to a setting with several families of varieties: For any integer $D\geq 1$ and any collection of sets $\Gamma_1,\ldots,\Gamma_j$ of low-degree…
This is the second of three papers about the Compression Theorem. We give proofs of Gromov's theorem on directed embeddings [M Gromov, Partial differential relations, Springer--Verlag (1986); 2.4.5 C'] and of the Normal Deformation Theorem…
We study a categorical condition on relations, which is a categorical formulation of J\'onsson's characterisation of congruence distributive varieties. Categories satisfying these conditions need not be varieties; for instance, the dual of…
We prove that the constraint languages invariant under a short sequence of J\'onsson terms (containing at most three non-trivial ternary terms) are tractable by showing that they have bounded width. This improves the previous result by Kiss…
Given a Schubert variety $\mathcal{S}$ contained in a Grassmannian $\mathbb{G}_{k}(\mathbb{C}^{l})$, we show how to obtain further information on the direct summands of the derived pushforward $R \pi_{*} \mathbb{Q}_{\tilde{\mathcal{S}}}$…