Related papers: A cancellativity criterion for presented monoids
A large class of positive finite presentations of the braid groups is found and studied. It is shown that no presentations but known exceptions in this class have the property that equivalent braid words are also equivalent under positive…
We introduce methods to study the combinatorics of the normal form of large random elements in Artin-Tits monoids. These methods also apply in an axiomatic framework that encompasses other monoids such as dual braid monoids.
We explain the sense in which a warping on a monoidal category is the same as a pseudomonad on the corresponding one-object bicategory, and we describe extensions of this to the setting of skew monoidal categories: these are a…
In this work, we provide a combinatorial formalism for dealing with the cancellations that have appeared recently in the context of dispersive PDEs with random initial data. The main idea is to transform iterated integrals encoded by…
We prove that the exponential growth rate of the regular language of penetration sequences is smaller than the growth rate of the regular language of normal form words, if the acceptor of the regular language of normal form words is…
We study applications of a general approach for arities and arizabilities of theories to group and monoid theories. It is proved that a theory of a group $G$ is aritizable if and only if $G$ is finite. It is shown that this criterion does…
The non-empty finite subsets of a multiplicatively written monoid form a monoid under setwise multiplication. The same holds for finite subsets containing the identity element. Partly due to their unusual arithmetic properties, these…
In this paper natural necessary and sufficient conditions for quantifier elimination of matrix rings $M_n(K)$ in the language of rings expanded by two unary functions, naming the trace and transposition, are identified. This is used…
We give a computational algorithm which decides if a braid is quasipositive or not. A braid is quasipositive if it's a product of conjuguates of generators. For this, we use the theory of Garside and the combinatorials properties of the…
Based on the recent work \cite{PII} we put forward a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations,…
We summerize the status of factorization hypothesis in the color-suppressed B meson decays : $B \to J/\psi K^{(*)}$. We present the general formalism for decay rates and polarization fractions with considering all possible non-factorizable…
Given a presentably symmetric monoidal $\infty$-category $\mathcal{C}$ and an $\mathbb{E}_{\infty}$-monoid $M$, we introduce and classify twisted graded categories, which generalize the Day convolution structure on $\mathrm{Fun}(M,…
A tentative proposal is demonstrated that there is a natural strategy to get rid of unphysical (UV) infinities in QFTs if one adopts the modern standard point of view that a fundamental theory that is complete and well-defined in all…
The sensitivity criterion is widely used in measuring the level of fine-tuning, although many examples show it doesn't work under certain circumstances. We discuss the mathematics behind the fine-tuning problems, explain the mathematical…
We consider the classical problem of determining the largest possible cardinality of a minimal presentation of a numerical monoid with given embedding dimension and multiplicity. Very few values of this cardinality are known. In addressing…
A cancellative commutative monoid is atomic if every non-invertible element factors into irreducibles. Under certain mild conditions on a positive algebraic number $\alpha$, the additive monoid $M_\alpha$ of the evaluation semiring…
Given a monoidal $\infty$-category $C$ equipped with a monoidal recollement, we give a simple criterion for an object in $C$ to be dualizable in terms of the dualizability of each of its factors and a projection formula relating them.…
We define specific multiplicities on the braid arrangement by using edge-bicolored graphs. To consider their freeness, we introduce the notion of bicolor-eliminable graphs as a generalization of Stanley's classification theory of free…
Perhaps it is not completely superfluous to remind that Clauser-Horne factorability, introduced in [1], is only necessary when \lambda, the hidden variable (HV), is sufficiently deterministic: for {M_i} a set of possible measurements…
In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…