✍ Scribed by Andrew Granville
No coin nor oath required. For personal study only.
Granville, A., On a paper of Agur, Fraenkel and Klein, Discrete Mathematics 94 (1991) 147-151. We count binary strings where the possible numbers of successive O's and l's are restricted.
For given sets A and B of positive integers define, for each n 2 1, S(A, B; n) to be the set of vectors (xl, x2, . . . ,x,J in (0, l}" which do not contain a subvector ( $9 xi+1 9 l --Jj+c, $+=+I ) of the form (1, 0, 0, . . . , 0, 0,l) (with c zeros) for any c$A or the form (O,l,l,.
. . , 1, 1,O) (with c CXS) for any c $ B (here the indices of the Xi's are taken (mod n)). (A vector in (0, l}" is called a 'binary string with n bits'). Let Y(A, B; n) be the number of elements in S(A, B; n)\
📜 SIMILAR VOLUMES
Ding, G., Disjoint circuits on a Klein bottle and a theorem on posets, Discrete Mathematics 112 (1993) 81-91. In this paper, we consider the problem of packing disjoint directed circuits in a digraph drawn on the Klein bottle or on the torus. We formulate a problem on posets which unifies all the p
## Abstract A general scheme for factorizing second‐order time‐dependent operators of mathematical physics is given, which allows a reduction of corresponding second‐order equations to biquaternionic equations of first order. Examples of application of the proposed scheme are presented for both con