Abstract. For an element w in the Weyl algebra generated by D and U with relation DU = UD + 1, the normally ordered form is w = ∑ ci,jU D . We demonstrate that the normal order coefficients ci,j of a word w are rook numbers on a Ferrers board. We use this interpretation to give a new proof of the rook factorization theorem, which we use to provide an explicit formula for the coefficients ci,j ....

This paper introduces a variation on the binomial coefficient that depends on a poset and interpolates between q-binomials and 1-binomials: a total order gives the usual q-binomial, and a poset with no relations gives the usual binomial coefficient. These coefficients arise naturally in the study of supercharacters of the finite groups of unipotent upper-triangular matrices, whose representatio...

Abstract We study L q -spectra of planar self-affine measures generated by diagonal matrices. introduce a new technique for constructing and understanding examples based on combinatorial estimates the exponential growth certain split binomial sums. Using this approach we disprove theorem Falconer Miao from 2007 conjecture 2008 concerning closed form expression generalised dimensions generic mea...

Abstract. The q-binomial coefficient is a polynomial in q. Given an integer t and a residue class r modulo t, a sieved q-binomial coefficient is the sum of those terms whose exponents are congruent to r modulo t. In this paper explicit polynomial identities in q are given for sieved q-binomial coefficients. As a limiting case, generating functions for the sieved partition function are found as ...