We demonstrate that categories of continuous actions topological monoids on discrete spaces are Grothendieck toposes. exhibit properties these toposes, giving a solution to the corresponding Morita-equivalence problem. characterize toposes in terms their canonical points. identify natural classes representatives with good properties, 'powder monoids' and then 'complete monoids', for monoids. Fi...

We introduce a shifted analog of the plactic monoid of Lascoux and Schützenberger, the shifted plactic monoid. It can be defined in two different ways: via the shifted Knuth relations, or using Haiman’s mixed insertion. Applications include: a new combinatorial derivation (and a new version of) the shifted Littlewood-Richardson Rule; similar results for the coefficients in the Schur expansion o...

Let Q be a quiver. M. Reineke and A. Hubery investigated the connection between the composition monoid CM(Q), as introduced by M. Reineke, and the generic composition algebra Cq(Q), as introduced by C. M. Ringel, specialised at q = 0. In this thesis we continue their work. We show that if Q is a Dynkin quiver or an oriented cycle, then C0(Q) is isomorphic to the monoid algebra QCM(Q). Moreover,...

for their help and suggestions. Special thanks go to J. Araujo for his mathematical suggestions. I would also like to acknowledge the support of the Centre of Algebra at the University of Lisbon, and of EPSRC grant number GR/S/56085/01. Colophon If you use the MONOID package, I would really appreciate it if you would let me know by sending me an email to [email protected]. If you notice that th...

We study the problem of testing whether a context-free language is included in a fixed set L0, where L0 is the language of words reducing to the empty word in the monoid defined by a complete string rewrite system. We prove that, if the monoid is cancellative, then our inclusion problem is polynomially reducible to the problem of testing equivalence of straight-line programs in the same monoid....

The notion of Σ-monoids is proposed by Fiore, Plotkin and Turi, to give abstract algebraic model of languages with variable binding and substitutions. In this paper, we give a free construction of Σ-monoids. The free Σ-monoid over a given presheaf serves a well-structured term language involving binding and substitutions. Moreover, the free Σ-monoid naturally contains interesting syntactic obje...

The order of hypersubstitutions, all idempotent elements on the monoid of all hypersubstitutions of type τ 2 were studied by K. Denecke and Sh. L. Wismath and all idempotent elements on the monoid of all hypersubstitutions of type τ 2, 2 were studied by Th. Changpas and K. Denecke. We want to study similar problems for the monoid of all generalized hypersubstitutions of type τ 2 . In this paper...

Let $n \in \mathbb{Z}^{+}$ and $X_{n}=\{1,2,\ldots,n\}$ be a finite set. $\mathcal ODCT_{n}$ the order-preserving order-decreasing full contraction mappings on $X_{n}$. It is well known that monoid. In this paper, we have found monoid rank presentation of ODCT_{n}$. particular, proved $n-1$ for $$ \geq 3$.

Motivated by the Babai conjecture and the Černý conjecture, we study the reset thresholds of automata with the transition monoid equal to the full monoid of transformations of the state set. For automata with n states in this class, we prove that the reset thresholds are upperbounded by 2n − 6n + 5 and can attain the value n(n−1) 2 . In addition, we study diameters of the pair digraphs of permu...