相关论文: Tropical linear representations of the Chinese mon…
Recent research of the author has given an explicit geometric description of free (two-sided) adequate semigroups and monoids, as sets of labelled directed trees under a natural combinatorial multiplication. In this paper we show that there…
This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial,…
We define a formal framework for the study of algebras of type Max-plus, Min-Plus, tropical algebras, and more generally algebras over a commutative idempotent semi-field. This work is motivated by the increasingly diversified use of these…
We study two dimensional and three dimensional tropical subrepresentations of the regular representation $\mathbb{B}[G]$ of a finite group over the tropical booleans, utilizing the theory of group representations over a fixed idempotent…
A transversal matroid $M$ of rank $r$ on $[n]$ can be associated to a family of binary matrices corresponding to different presentations of $M$. We describe those matrices which arise from unique maximal presentations of size $r$- giving a…
We give a new and conceptually straightforward proof of the well-known presentation for the Temperley-Lieb algebra, via an alternative new presentation. Our method involves twisted semigroup algebras, and we make use of two apparently new…
We make the classical Dickenstein-Sessa canonical representation in local moderate cohomology explicit by an integral formula. We also provide a similar representation of the higher local moderate cohomology groups. The results are related…
We study the tropicalization of the image of the cone of positive definite matrices under the principal minors map. It is a polyhedral subset of the set of $M$-concave functions on the discrete $n$-dimensional cube. We show it coincides…
We exhibit faithful representations of the hypoplactic, stalactic, taiga, sylvester, Baxter and right patience sorting monoids of each finite rank as monoids of upper triangular matrices over any semiring from a large class including the…
We study the free objects in the variety of semigroups and variety of monoids generated by the monoid of all $n \times n$ upper triangular matrices over a commutative semiring. We obtain explicit representations of these, as multiplicative…
We study the max-plus or tropical analogue of the notion of polar: the polar of a cone represents the set of linear inequalities satisfied by its elements. We establish an analogue of the bipolar theorem, which characterizes all the…
In this paper we give a spinorial representation of submanifolds of any dimension and codimension into Lie groups equipped with left invariant metrics. As applications, we get a spinorial proof of the Fundamental Theorem for submanifolds…
Let $\mathscr{C}_{+}(a,b)$ be the submonoid of the bicyclic monoid which is studied in \cite{Makanjuola-Umar=1997}. We describe monoid endomorphisms of the semigroup $\mathscr{C}_{+}(a,b)$ which are generated by the family of all…
This paper uses the combinatorics of Young tableaux to prove the plactic monoid of infinite rank does not satisfy a non-trivial identity, by showing that the plactic monoid of rank $n$ cannot satisfy a non-trivial identity of length less…
In this paper, we characterize the monoid of endomorphisms of the semigroup of all monotone full transformations of a finite chain, as well as the monoids of endomorphisms of the semigroup of all monotone partial transformations and of the…
Given a family of parameterized algebraic curves over a strictly semistable pair, we show that the simultaneous tropicalization of the curves in the family forms a family of parameterized tropical curves over the skeleton of the strictly…
In this paper the linear representations of analytic Moufang loops are investigated. We prove that every representation of semisimple analytic Moufang loop is completely reducible and find all nonassociative irreducible representations. We…
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.
Our aim in this paper is to initiate the study of exponent semigroups for rational matrices. We prove that every numerical semigroup is the exponent semigroup of some rational matrix. We also obtain lower bounds on the size of such matrices…
We show that the algebra of the coloured rook monoid $R_n^{(r)}$, {\em i.e.} the monoid of $n \times n$ matrices with at most one non-zero entry (an $r$-th root of unity) in each column and row, is the algebra of a finite groupoid, thus is…