We derive necessary conditions related to the notions, in additive combinatorics, of Sidon sets and sum-free sets, on those exponents d ∈ Z/(2 − 1)Z which are such that F (x) = x is an APN function over F2n (which is an important cryptographic property). We study to which extent these new conditions may speed up the search for new APN exponents d. We also show a new connection between APN expon...

A reciprocal polynomial g(x) ∈ Z[x] is such that g(0) 6= 0 and if g(α) = 0 then g(1/α) = 0. The non-reciprocal part of a monic polynomial f(x) ∈ Z[x] is f(x) divided by the product of its irreducible monic reciprocal factors (to their multiplicity). This paper presents an algorithm for testing the irreducibility of the nonreciprocal part of a 0, 1-polynomial (a polynomial having each coefficien...

In the case that k = n− 1, the polynomial Pn,k(x) takes the form Pn,n−1(x) = (x+ 1) n − x. If n is not a prime, Pn,n−1(x) is reducible over Q. If n = p is prime, the polynomial Pn,n−1(x) = Pp,p−1(x) is irreducible as Eisenstein’s criterion applies to the reciprocal polynomial xPp,p−1(1/x). This note concerns the irreducibility of Pn,k(x) in the case where 1 ≤ k ≤ n− 2. Computations for n ≤ 100 ...

Plasmids capable of undergoing genetic exchange in mitotically dividing Saccharomyces cerevisiae cells were used to measure the length of gene conversion events, to determine patterns of coconversion when multiple markers were present, and to correlate the incidence of reciprocal recombination with the length of conversion tracts. To construct such plasmids, restriction site linkers were insert...

Homologous recombination is essential for accurate chromosome segregation during meiosis in most sexual organisms. Meiotic recombination is initiated by the formation of DSBs (DNA double-strand breaks) made by the Spo11 protein. We review here recent findings pertaining to protein-protein interactions important for DSB formation, the mechanism of an early step in the processing of Spo11-generat...

recently, hua et al. defined a new topological index based on degrees and inverse ofdistances between all pairs of vertices. they named this new graph invariant as reciprocaldegree distance as 1{ , } ( ) ( ( ) ( ))[ ( , )]rdd(g) = u v v g d u  d v d u v , where the d(u,v) denotesthe distance between vertices u and v. in this paper, we compute this topological index forgrassmann graphs.

Reciprocal series are employed to systematically review convolution sums, orthogonality relations, recurrence relations and reciprocal formulae for several classical number sequences, such as binomial coefficients, Stirling numbers, Bernoulli Euler numbers.

illustration, the prime reciprocal of 1/7 is , and the prime reciprocal sequence is considered to be 142857. The period of this sequence is 6. Since the maximum length of the period can be (p-1), this is an example of a maximum-length d-sequence. But a prime reciprocal sequence that is maximum length in one base need not be maximum length in another base. Thus the binary prime reciprocal sequen...

Reciprocal customers may disproportionately improve the performance of markets for experience goods. Reciprocal customers reward (punish) ...rms for providing good (bad) quality by upholding (terminating) the customer relation. This may induce ...rms to provide good quality. Reciprocal customers can be social multipliers in two ways. First, reciprocal customers cause a positive externality for ...