Symmetric identity for polynomial sequences satisfying A′ n +1(x) = (n + 1)An (x)

On Sequences G n Satisfying G n = ( d + 2 ) G n − 1 − G n − 2 Ricky X . F . Chen Center for Combinatorics LPMC

In this note, we study a class of sequences Gn satisfying Gn = (d+2)Gn−1 −Gn−2. Note that the Fibonacci numbers Gn = F2n, n > 1 and Gn = F2n+1, n > 0 occur when d = 1 with suitable initial conditions. We present a general interpretation for this class of sequences in terms of ordered trees which we count by nodes and outdegrees. Further more, several other related integer sequences are also stu...

Representation Theory of Noetherian Hopf Algebras Satisfying a Polynomial Identity

A class of Noetherian Hopf algebras satisfying a polynomial identity is axiomatised and studied. This class includes group algebras of abelian-by-nite groups, nite dimensional restricted Lie algebras, and quantised enveloping algebras and quantised function algebras at roots of unity. Some common homological and representation-theoretic features of these algebras are described, with some indica...

The Nature of Halogen Bonds in [N∙∙∙X∙∙∙N]+ Complexes: A Theoretical Study

     The effects of substituents on the symmetry and the nature of halogen bonds in [N∙∙∙X∙∙∙N]+-type systems are presented for the YC5H4N∙∙∙X∙∙∙NC5H5 (Y = NO2, CN, H, CH3, OCH3, OH, NH2, X = Cl, Br, I) complexes. Some structural parameters, energy data and electronic properties were explored with...

Semigroups Satisfying xm+n = xn

We summarize recent results on semigroups satisfying the identity x = x, for n 0 and m 1, and some rewrite techniques that have contributed to their investigation.

Constructing O(n log n) Size Monotone Formulae for the k-th Elementary Symmetric Polynomial of n Boolean Variables