The MacMahon R-matrix

The quantum MacMahon Master Theorem.

We state and prove a quantum generalization of MacMahon's celebrated Master Theorem and relate it to a quantum generalization of the boson-fermion correspondence of physics.

The partitioned R - matrix

Some generalizations of the MacMahon Master Theorem

We consider a number of generalizations of the β-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations or derangements over matrix or submatrix indices.

Enhancing an R-matrix

In order to construct a representation of the tangle category one needs an enhanced R-matrix. In this paper we define a sufficient and necessary condition for enhancement that can be checked easily for any R-matrix. If the R-matrix can be enhanced, we also show how to construct the additional data that define the enhancement. As a direct consequence we find a sufficient condition for the constr...

determinant of the hankel matrix with binomial entries

abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.