We attach with every finite, involutive, nondegenerate set-theoretic solution of the Yang–Baxter equation a finite group that plays for the associated structure group the role that a finite Coxeter group plays for the associated Artin–Tits group.

We introduce the decreasing proof order. It orders a conversion above another conversion if the latter is obtained by filling any peak in the former by a decreasing diagram. The result is developed in the setting of involutive monoids.

We give some new Wilf equivalences for signed patterns which allow the complete classification of signed patterns of lengths three and four. The problem is considered for pattern avoidance by general as well as involutive signed permutations.

The Frobenius theorem is extended from supermanifolds to N-graded manifolds. It is shown, both for super and N-graded manifolds, that the characteristic distribution of a presymplectic submanifold is involutive and hence integrable.

Let C be the propositional calculus given by a standard SBL-algebra; C is obtained from C by adding an involutive negation, with axioms and deduction rules as in [4]. Then C is coNP-complete.

Abstract An algebraic proof is presented for the finite strong standard completeness of Involutive Uninorm Logic with Fixed Point ( $${{\mathbf {IUL}}^{fp}}$$ IUL fp ). It may provide a first step towards settling problem $${\mathbf {IUL}}$$ , pos...