Abstract. We introduce the Hopf algebra of uniform block permutations and show that it is self-dual, free, and cofree. These results are closely related to the fact that uniform block permutations form a factorizable inverse monoid. This Hopf algebra contains the Hopf algebra of permutations of Malvenuto and Reutenauer and the Hopf algebra of symmetric functions in non-commuting variables of Ge...

Gleason has described the general form that the weight distribution of a self-dual code over GF(2) and GF(3) can have. We give an explicit formula for this weight distribution when the minimum distance d between codewords is made as large as possible. It follows that for self-dual codes of length n over GF(2) with all weights divisible by 4, d ~ 4[n/24] + 4; and for self-dual codes over GF(3), ...

in this work, we proposed an efective method based on cubic and pantic b-spline scaling functions to solve partial differential equations of frac- tional order. our method is based on dual functions of b-spline scaling func- tions. we derived the operational matrix of fractional integration of cubic and pantic b-spline scaling functions and used them to transform the mentioned equations to a ...

For any two graphs F and G, let hom(F,G) denote the number of homomorphisms F → G, that is, adjacency preserving maps V (F ) → V (G) (graphs may have loops but no multiple edges). We characterize Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary. Email: [email protected]. Research sponsored by OTKA Grant No. 67867. CWI and University of Amsterdam, Amsterdam, The Netherlands....

A bent function is called self-dual if it is equal to its dual. It is called anti-self-dual if it is equal to the complement of its dual. A spectral characterization in terms of the Rayleigh quotient of the Sylvester Hadamard matrix is derived. Bounds on the Rayleigh quotient are given for Boolean functions in an odd number of variables. An efficient search algorithm based on the spectrum of th...