We enumerate bijectively the family of involutive Baxter permutations according to various parameters; in particular we obtain an elementary proof that the number of involutive Baxter permutations of size 2n with no fixed points is 3·2 n−1

When analysing general systems of PDEs, it is important first to find the involutive form of the initial system. This is because the properties of the system cannot in general be determined if the system is not involutive. We show that the notion of involutivity is also interesting from the numerical point of view. The use of the involutive form of the system allows one to consider quite genera...

We consider the check of the involutive basis property in a polynomial context. In order to show that a finite generating set F of a polynomial ideal I is an involutive basis one must confirm two properties. Firstly, the set of leading terms of the elements of F has to be complete. Secondly, one has to prove that F is a Gröbner basis of I. The latter is the time critical part but can be acceler...

This note analyzes in terms of categorial proof theory some standard assumptions about negation in the absence of any other connective. It is shown that the assumptions for an involutive negation, like classical negation, make a kind of adjoint situation, which is named involutive adjunction. The notion of involutive adjunction amounts in a precise sense to adjunction where an endofunctor is ad...

Many interesting geometric structures can be defined by specifying a smooth subbundle V of the complexified tangent bundle of the underlying smooth manifold, subject to an integrability condition. Examples include foliations, complex structures, and CR structures. In general such structures are called involutive, or formally integrable, and their study has been the starting point of far-reachin...

This paper investigates connections between algebraic structures that are common in theoretical computer science and algebraic logic. Idempotent semirings are the basis of Kleene algebras, relation algebras, residuated lattices and bunched implication algebras. Extending a result of Chajda and Länger, we show that involutive residuated lattices are determined by a pair of dually isomorphic idem...

One of the recent advances in Functional Analysis has been the introduction of the notion of an (abstract) operator space. Proponents of this theory have, since its inception, maintained that it provides a much more solid " foundations " for Operator Algebra than the more traditional theory of Banach spaces. In this paper, we show that there exists a (non-trivial) involutive monoidal structure ...

Recently, Zharkov and Blinkov introduced the notion of involutive bases of polynomial ideals. This involutive approach has its origin in the theory of partial di erential equations and is a translation of results of Janet and Pommaret. In this paper we present a pure algebraic foundation of involutive bases of Pommaret type. In fact, they turn out to be generalized left Grobner bases of ideals...