The wealth of beautiful combinatorics that arise in the representation theory of the symmetric group is well-known. In this paper, we analyze the representations of a related algebraic structure called the rook monoid from a combinatorial angle. In particular, we give a combinatorial construction of the irreducible representations of the rook monoid. Since the rook monoid contains the symmetric...

We generalize the word problem for groups, the formal language of all words in the generators that represent the identity, to inverse monoids. In particular, we introduce the idempotent problem, the formal language of all words representing idempotents, and investigate how the properties of an inverse monoid aer related to the formal language properties of its idempotent problem. In particular,...

In this paper, all the monoids considered are commutative. If S is a monoid generated by {m1, . . . ,mn}, then S is isomorphic to a quotient monoid of N by the kernel congruence σ of the map φ : N → S, φ(k1, . . . , kn) = ∑n i=1 kimi. Under this setting, a finite presentation for S is a finite subset ρ of Nn×Nn such that the congruence generated by ρ is equal to σ. Rédei proves in [5] that ever...

All semigroups and monoids except free monoids and free groups are assumed finite in this paper. A monoid M divides a monoid N if M is a quotient of a submonoid of N . The set of idempotents of a monoid M is denoted E(M). The word “variety” will be used for pseudo-variety — that is, a collection of finite monoids closed under division and finite direct product. A block group is a monoid such th...

In this paper we introduce and study the theories of pseudo links singular in Solid Torus, ST. Pseudo are with some missing crossing information that naturally generalize notion knot diagrams, have potential use molecular biology, while contain a finite number self-intersections. We consider ST set up appropriate topological theory order to construct invariants for these types particular, formu...

A partial monoid P is a set with a partial multiplication × (and total identity 1P ) which satisfies some associativity axiom. The partial monoid P may be embedded in the free monoid P ∗ and the product × is simulated by a string rewriting system on P ∗ that consists in evaluating the concatenation of two letters as a product in P , when it is defined, and a letter 1P as the empty word ǫ. In th...

Given a finitely presented monoid and a homotopy base for the monoid, and given an arbitrary Schützenberger group of the monoid, the main result of this paper gives a homotopy base, and presentation, for the Schützenberger group. In the case that the R-class R of the Schützenberger group G (H) has only finitely many H -classes, and there is an element s of the multiplicative right pointwise sta...