相关论文: The well-ordering of dual braid monoids

Consider the ring $R:=\Q[\tau,\tau^{-1}]$ of Laurent polynomials in the variable $\tau$. The Artin's Pure Braid Groups (or Generalized Pure Braid Groups) act over $R,$ where the action of every standard generator is the multiplication by…

We show that the restriction of the Dehornoy ordering to an appropriate free subgroup of the three-strand braid group defines a left ordering of the free group on k generators, k>1, that has no convex subgroups.

Lattice path matroids form a subclass of transversal matroids and were introduced by Bonin, de Mier and Noy. Transversal matroids are not well-quasi-ordered, even when the branch-width is restricted. Though lattice path matroids are not…

We show that every braiding on a monoidal bicategory induces a monoidal structure on its bicategory of monoids, such that if the former is sylleptic or symmetric then the latter is braided or symmetric, respectively. This extends a classic…

A family of partial orders in the free monoid of words, induced from a partial order in alphabet, is presented. The induced orders generalize the chronological posets that have been defined for the two-letter alphabet only, and the…

Empirical properties of generating systems for complex reflection groups and their braid groups have been observed by Orlik-Solomon and Brou\'e-Malle-Rouquier, using Shephard-Todd classification. We give a general existence result for…

Inspired by methods in prime characteristic in commutative algebra, we introduce and study combinatorial invariants of seminormal monoids. We relate such numbers with the singularities and homological invariants of the semigroup ring…

In this paper we define a monoid of pseudo braids and prove that this monoid is isomorphic to a singular braid monoid. We also prove an analogue of Markov's theorem for pseudo braids.

We show that there exist ordered orthogonal arrays, whose sizes deviate from the Rao bound by a factor that is polynomial in the parameters of the ordered orthogonal array. The proof is nonconstructive and based on a probabilistic method…

In the present paper we introduce a lattice-ordered partial monoid structure on a suitable set of multilayer networks. We first study a kind of mappings that preserve the partial order and describe the order structure. After that we define…

We classify cocovers and covers of a given element of the double affine Weyl semigroup W with respect to the Bruhat order, specifically when W is associated to a finite root system that is irreducible and simply laced. We show two…

In Artin-Tits groups attached to Coxeter groups of spherical type, we give a combinatorial formula to express the simple elements of the dual braid monoids in the classical Artin generators. Every simple dual braid is obtained by lifting an…

In this paper, we introduce D-star order, T-star order and P-star order on the class of dual matrices. By applying matrix decomposition and dual generalized inverses, we discuss properties, characterizations and relations among these…

Extending the works of Alladi and Sweeting and Woo, we state and prove the general higher order duality between prime ideals in number rings. We then use the second order duality to obtain the a new formula for the Chebotarev Density…

In this article combinatorial aspects of normal ordering annihilation and creation operators of a multi-mode boson system are discussed. The modes are assumed to be coupled since otherwise the problem of normal ordering is reduced to the…

In a highly influential paper, Bidigare, Hanlon and Rockmore showed that a number of popular Markov chains are random walks on the faces of a hyperplane arrangement. Their analysis of these Markov chains took advantage of the monoid…

Consider the ring R:=\Q[\tau,\tau^{-1}] of Laurent polynomials in the variable \tau. The Artin's Pure Braid Groups (or Generalized Pure Braid Groups) act over R, where the action of every standard generator is the multiplication by \tau. In…

The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the properties of dual dimonoids. In the class of noncommutative…

This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…

We introduce a monoidal category of corings using two different notions of corings morphisms. The first one is the (right) coring extensions recently introduced by T. Brzezi\'nski in [2], and the anther is the usual notion of morphisms…