The (shifted) plactic monoid. The celebrated Robinson-Schensted-Knuth correspondence (14) is a bijection between words in a linearly ordered alphabet X = {1 < 2 < 3 < · · · } and pairs of Young tableaux with entries in X . More precisely, each word corresponds to a pair consisting of a semistandard insertion tableau and a standard recording tableau. The words producing a given insertion tableau...

In (Golchin A. and Rezaei P., Subpullbacks and flatness properties of S-posets. Comm. Algebra. 37: 1995-2007 (2009)) study was initiated of flatness properties of right -posets  over a pomonoid  that can be described by surjectivity of  corresponding to certain (sub)pullback diagrams and new properties such as  and  were discovered. In this article first of all we describe po-flatness propertie...

We introduce a generic type system for the synchronouspolyadic -calculus, allowing us to mechanize the analysis of input/output capabilities of mobile processes. The parameter of the generic type system is a lattice-ordered monoid, the elements of which are used to describe the capabilities of channels with respect to their input/outputcabilities. The type system can be instantiated in order to...

These notes (still in draft form) arose from a challenge arising in the discussion of FMathL on the n-Category Café. I had claimed: “ For example, one can express with this naturally (and every mathematician immediately understands without the need for explanations) that ordered monoids are the objects in the intersection of Order and Monoid satisfying the compatibility relation R (suitably def...

Fuzzy logic generalises classical logic; in addition to the latter’s truth values “false” and “true”, the former allows also intermediary truth degrees. The conjunction is, accordingly, interpreted by an operation acting on a chain, making the set of truth degrees into a totally ordered monoid. We present in this chapter two different ways of investigating this type of algebras. We restrict to ...

Given a finite alphabet X and an ordering ≺ on the letters, the map σ≺ sends each monomial on X to the word that is the ordered product of the letter powers in the monomial. Motivated by a question on Gröbner bases, we characterize ideals I in the free commutative monoid (in terms of a generating set) such that the ideal 〈σ≺(I)〉 generated by σ≺(I) in the free monoid is finitely generated. Wheth...

We give a combinatorial description of a finite Thurston type ordering < on the dual braid monoid B n by introducing the C-normal form and prove that the order-type of the well-ordered set (B n , <) is ωω n−2 . The C-normal form can be seen as a generalization of the rotating normal form defined by Fromentin and it is also a natural extension of C-normal form of the positive braid monoids defin...

Let us assume there exists an unconditionally solvable co-normal prime. Recent interest in Fermat, globally Deligne, almost Noetherian moduli has centered on computing algebraically embedded, hyper-complete measure spaces. We show that there exists an ordered invariant monoid equipped with a compactly unique homeomorphism. So is it possible to derive geometric homomorphisms? A. S. Sasaki [14] i...

We give an combinatorial description of a finite Thurston type ordering <T of the positive braid monoid B + n by introducing the C-normal form. The C-normal form can be seen as a generalization of Burckel’s normal form and Dehornoy’s Φ-normal form. Using this description, we determine the order type of well-ordered set (Bn, <T ) for all finite Thurston type orderings <T .

Residuation theory concerns the study of partially ordered algebraic structures, most often monoids, equipped with a weak inverse for monoidal operator. One its area application has been constraint programming, whose key requirement is presence an aggregator operator combining preferences. Given residuated monoid preferences, paper first shows how to build new (possibly infinite) tuples, which ...