Asymptotic Analysis of q-Recursive Sequences.

For an integer q ≥ 2 , a q-recursive sequence is defined by recurrence relations on subsequences of indices modulo some powers of q. In this article, q-recursive sequences are studied and the asymptotic behavior of their summatory functions is analyzed. It is shown that every q-recursive sequence is q-regular in the sense of Allouche and Shallit and that a q-linear representation of the sequence can be computed easily by using the coefficients from the recurrence relations. Detailed asymptotic results for q-recursive sequences are then obtained based on a general result on the asymptotic analysis of q-regular sequences. Three particular sequences are studied in detail: We discuss the asymptotic behavior of the summatory functions ofStern's diatomic sequence,the number of non-zero elements in some generalized Pascal's triangle andthe number of unbordered factors in the Thue-Morse sequence. For the first two sequences, our analysis even leads to precise formulæ without error terms.

Asymptotic Analysis of Regular Sequences.

In this article, q-regular sequences in the sense of Allouche and Shallit are analysed asymptotically. It is shown that the summatory function of a regular sequence can asymptotically be decomposed as a finite sum of periodic fluctuations multiplied by a scaling factor. Each of these terms corresponds to an eigenvalue of the sum of matrices of a linear representation of the sequence; only the eigenvalues of absolute value larger than the joint spectral radius of the matrices contribute terms which grow faster than the error term. The paper has a particular focus on the Fourier coefficients of the periodic fluctuations: they are expressed as residues of the corresponding Dirichlet generating function. This makes it possible to compute them in an efficient way. The asymptotic analysis deals with Mellin-Perron summations and uses two arguments to overcome convergence issues, namely Hölder regularity of the fluctuations together with a pseudo-Tauberian argument. Apart from the very general result, three examples are discussed in more detail:sequences defined as the sum of outputs written by a transducer when reading a q-ary expansion of the input;the amount of esthetic numbers in the first N natural numbers; andthe number of odd entries in the rows of Pascal's rhombus. For these examples, very precise asymptotic formulæ are presented. In the latter two examples, prior to this analysis only rough estimates were known.

Target Meaning-Making of Workplace Incivility Based on Perceived Personality Similarity with Perpetrators.

Target meaning-making of incivility (i.e., the ways targets assess uncivil events) has received attention as an important mediating mechanism in explaining the varied outcomes of incivility. The present study draws on person-environment (PE) fit theory, as well as the similarity-attraction paradigm and repulsion hypothesis, to uncover how perceived personality (dis)similarity affects both cognitive (i.e., attribution, negative appraisal) and emotional reactions (i.e., hostility) to incivility. Specifically, we examine whether incongruence between target personality and perceived perpetrator personality worsens target meaning-making (vice versa for personality congruence). Study 1 (N = 479 employees) addressed (dis)similarity in agreeableness, while Study 2 (N = 296 working adults) addressed (dis)similarity in neuroticism. Based on polynomial regressions with response surface modeling, the results generally supported the hypotheses. Along the line of dissimilarity, targets often assessed (i.e., attributed intent to, appraised, reacted emotionally to) uncivil events more negatively when they perceived personality dissimilarity with perpetrators. However, similarity in personality did not always have the opposite effect by buffering against negative assessments; meaning-making was worse when both parties scored high on neuroticism. Implications for workplace incivility and PE fit literatures are discussed, along with practical implications that highlight information elaboration and perspective taking.

Analysis of the width-[Formula: see text] non-adjacent form in conjunction with hyperelliptic curve cryptography and with lattices.

In this work the number of occurrences of a fixed non-zero digit in the width-[Formula: see text] non-adjacent forms of all elements of a lattice in some region (e.g. a ball) is analysed. As bases, expanding endomorphisms with eigenvalues of the same absolute value are allowed. Applications of the main result are on numeral systems with an algebraic integer as base. Those come from efficient scalar multiplication methods (Frobenius-and-add methods) in hyperelliptic curves cryptography, and the result is needed for analysing the running time of such algorithms. The counting result itself is an asymptotic formula, where its main term coincides with the full block length analysis. In its second order term a periodic fluctuation is exhibited. The proof follows Delange's method.

Sylow p-groups of polynomial permutations on the integers mod [Formula: see text].

We enumerate and describe the Sylow p-groups of the groups of polynomial permutations of the integers mod [Formula: see text] for [Formula: see text] and of the pro-finite group which is the projective limit of these groups.

On linear combinations of units with bounded coefficients and double-base digit expansions.

Let [Formula: see text] be the maximal order of a number field. Belcher showed in the 1970s that every algebraic integer in [Formula: see text] is the sum of pairwise distinct units, if the unit equation [Formula: see text] has a non-trivial solution [Formula: see text]. We generalize this result and give applications to signed double-base digit expansions.