Related papers: Enumeration of m-Endomorphisms

Every semigroup which is a finite disjoint union of copies of the free mono- genic semigroup (natural numbers under addition) has soluble word prob- lem and soluble membership problem. Efficient algorithms are given for both problems.

The sequence of partial sums of Fibonacci numbers, beginning with $2$, $4$, $7$, $12$, $20$, $33,\dots$, has several combinatorial interpretations (OEIS A000071). For instance, the $n$-th term in this sequence is the number of length-$n$…

For a finite field k and a triple of integers g \ge r \ge s \ge 0, we count the number of semilinear endomorphisms of a g-dimensional k-vector space which have rank r and stable rank s. Such endomorphisms show up naturally in the…

We study endomorphisms of a free group of finite rank by means of their action on specific sets of elements. In particular, we prove that every endomorphism of the free group of rank 2 which preserves an automorphic orbit (i.e., acts ``like…

We prove that a homomorphism between free groups of finite rank equipped with the bi-invariant word metrics is a quasi-isometry if and only if it is an isomorphism.

Motivated by a problem on the dynamics of compositions of plane hyperbolic isometries, we prove several fundamental results on semigroups of isometries, thought of as real M\"obius transformations. We define a semigroup $S$ of M\"obius…

We study almost symmetric semigroups generated by odd integers. If the embedding dimension is four, we characterize when a symmetric semigroup that is not complete intersection or a pseudo-symmetric semigroup is generated by odd integers.…

We prove that, although it is undecidable if a subgroup fixed by an automorphism intersects nontrivially an arbitrary subgroup of $F_n\times F_m$, there is an algorithm that, taking as input a monomorphism and an endomorphism of $F_n\times…

We are interested in formulas for the number of elements in certain classes of numerical semigroups

Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…

Every semigroup containing an ideal subgroup is called a homogroup, and it is a grouplike if and only if it has only one central idempotent. On the other hand, a class of algebraic structures covering group-$e$-semigroups…

We investigate endomorphism semirings of a finite semilattice with one least element and one greatest element such that all the other elements form an antichain. We construct some new finite simple semirings. Keywords: endomorphism…

We show that the free construction from multicategories to permutative categories is a categorically-enriched non-symmetric multifunctor. Our main result then shows that the induced functor between categories of algebras is an equivalence…

We derive polynomial identities of arbitrary degree $n$ for syzygies degrees of numerical semigroups S_m=<d_1,...,d_m> and show that for n>=m they contain higher genera G_r=\sum_{s\in Z_>\setminus S_m}s^r of S_m. We find a number…

Lists of equivalence classes of words under rotation or rotation plus reversal (i.e., necklaces and bracelets) have many uses, and efficient algorithms for generating these lists exist. In combinatorial group theory elements of a group are…

The Mordell-Lang conjecture describes the intersection of a finitely generated subgroup with a closed subvariety of a semiabelian variety. Equivalently, this conjecture describes the intersection of closed subvarieties with the set of…

A free semigroupoid algebra is the closure of the algebra generated by a TCK family of a graph in the weak operator topology. We obtain a structure theory for these algebras analogous to that of free semigroup algebra. We clarify the role…

Two factorizations of a permutation into products of cycles are equivalent if one can be obtained from the other by repeatedly interchanging adjacent disjoint factors. This paper studies the enumeration of equivalence classes under this…

A quasi-automatic semigroup is defined by a finite set of generators, a rational (regular) set of representatives, such that if a is a generator or neutral, then the graph of right multiplication by a on the set of representatives is a…

We classify (up to quasi-isomorphism) the free differential modules whose homology is equal to a given module $M$ by developing a theory for deforming an arbitrary free complex into a differential module. We use an iterative approach to…