Using a reconstituted system containing genomic DNA and purified proteins from yeast, Krietenstein et al. uncover the direct contributions of key factors in nucleosome positioning and conceptualize the process into four distinct stages.

We study similarity classes of point configurations in R. Given a finite collection of points, a well-known question is: How high does the Hausdorff dimension dimH(E) of a compact set E ⊂ R, d ≥ 2, need to be to ensure that E contains some similar copy of this configuration? We prove results for a related problem, showing that for dimH(D) sufficiently large, E must contain many point configurat...

Following Jens Voß [9], let T (n, k) be the number of k-tuples u = (u1, u2, . . . , uk) with 0 ≤ u1 ≤ u2 ≤ · · · ≤ uk ≤ n− 1 such that ∑ j uj ≡ 0 mod n. Stated another way, T (n, k) is the number of ways to write 0 as a sum of k elements of Z/nZ. Voß calls u a modular partition of n into k parts. He computed the numbers T (n, k) for n+ k ≤ 20, and part of his table is shown here (the rows corre...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 29 September 2020Accepted: 16 May 2021Published online: 13 2021Keywordscombinatorics, Catalan, unimodal, cyclic sievingAMS Subject Headings05E10, 16G99, 20C30Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Society for Industrial and Applied Mathe...

Configurations are necklaces with prescribed numbers of red and black beads. Among all possible configurations, the regular one plays an important role in many applications. In this paper, several aspects of regular configurations are discussed, including construction, uniqueness, symmetry group and the link with balanced words. Another model of configurations is the polygons formed by a given ...

We develop a fast algorithm for listing all necklaces with &xed content. By &xed content, we mean the number of occurrences of each alphabet symbol is &xed. Initially, we construct a simple but ine4cient algorithm by making some basic modi&cations to a recursive necklace generation algorithm. We then improve it by using two classic combinatorial optimization techniques. An analysis using straig...

Single-track Gray codes are cyclic Gray codes with codewords of length n, such that all the n tracks which correspond to the n distinct coordinates of the codewords are cyclic shifts of the first track. We investigate the structure of such binary codes and show that there is no such code with 2n codewords when n is a power of 2. This implies that the known codes with 2n 2n codewords, when n is ...