The maximally clustered permutations are characterized by avoiding the classical permutation patterns {3421, 4312, 4321}. This class contains the freely braided permutations and the fully commutative permutations. In this work, we show that the generating functions for certain fully commutative pattern classes can be transformed to give generating functions for the corresponding freely braided ...

no-bahar watershed is located, south of khorasan razavi province. geologically, the study area is a part of central iran zone. the rock units are late mesozoic and cenozoic in age in this watershed. no-babhar watershed includes several channels, which among them, only two main channels, motr-abad and solh-abad, have been studied. these rivers are mostly, braided channel in style, with high grad...

We present an untyped linear lambda calculus with braids, the corresponding combinatory logic, and semantic models given by crossed G-sets.

We give a pedagogical introduction to integration techniques appropriate for non-commutative spaces while presenting some new results as well. A rather detailed discussion outlines the motivation for adopting the Hopf algebra language. We then present some trace formulas for the integral on Hopf algebras and show how to treat the ∫ 1 = 0 case. We extend the discussion to braided Hopf algebras r...

We show that the braided tensor product algebra A1⊗A2 of two module algebras A1,A2 of a quasitriangular Hopf algebraH is equal to the ordinary tensor product algebra of A1 with a subalgebra of A1⊗A2 isomorphic to A2, provided there exists a realization of H within A1. In other words, under this assumption we construct a transformation of generators which ‘decouples’ A1,A2 (i.e. makes them commu...

We briefly report on our result [9] that the braided tensor product algebra of two module algebras A1,A2 of a quasitriangular Hopf algebra H is equal to the ordinary tensor product algebra of A1 with a subalgebra isomorphic to A2 and commuting with A1, provided there exists a realization of H within A1. As applications of the theorem we consider the braided tensor product algebras of two or mor...

Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R4 can be described as certain 2-morphisms in the 2-category of ‘2-tangles in 4 dimensions’. Using the work of Carter, Rieger and Saito, we prove that this 2-category is the ‘free semistrict braided monoidal 2-category with duals on one un...