نتایج جستجو برای: schinzel equation
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Schinzel-Giedion syndrome (SGS) is a rare autosomal dominant disorder that results in facial dysmorphism, multiple congenital anomalies, and an increased risk of malignancy. Recently, using exome sequencing, de novo heterozygous mutations in the SETBP1 gene have been identified in patients with SGS. Most affected individuals do not survive after childhood because of the severity of this disorde...
We observe that five polynomial families have all of their roots on the unit circle. We prove the statements explicitly for four of the polynomial families. The polynomials have coefficients which involve Bernoulli numbers, Euler numbers, and the odd values of the Riemann zeta function. These polynomials are closely related to the Ramanujan polynomials, which were recently introduced by Murty, ...
An order-s Davenport-Schinzel sequence over an n-letter alphabet is one avoiding immediate repetitions and alternating subsequences with length s+2. The main problem is to determine the maximum length of such a sequence, as a function of n and s. When s is fixed this problem has been settled (see Agarwal, Sharir, and Shor [1], Nivasch [12] and Pettie [15]) but when s is a function of n, very li...
which give the arithmetic and the geometric means of the first n values of the Euler function, respectively, are uniformly distributed modulo 1. A. Schinzel modified these questions by asking whether these sequences are dense modulo 1. This question was repeated at the meeting on Uniform Distribution in Luminy in January 2008. In this paper, we give an affirmative answer to Schinzel’s question....
Let Ψs(n) be the extremal function of order-s Davenport-Schinzel sequences over an n-letter alphabet. Together with existing bounds due to Hart and Sharir (s = 3), Agarwal, Sharir, and Shor (s = 4, lower bounds on s ≥ 6), and Nivasch (upper bounds on even s), we give the following essentially tight bounds on Ψs(n) for all s: Ψs(n) = n s = 1
http://jbx.sagepub.com/content/10/1/36 The online version of this article can be found at: DOI: 10.1177/1087057104270269 2005 10: 36 J Biomol Screen Thomas Herget Freudenreich, Gaby Holzer, Sieglinde Schinzel, Thomas Stamminger, Matthias Stein-Gerlach, Manfred Marschall and Helmut Mett, Kerstin Hölscher, Heidrun Degen, Christina Esdar, Birgit Felden De Neumann, Birgit Flicke, Tatjana Kinase Ass...
For a prime p, we call a non-empty subset S of the group Fp balanced if every element of S is the midterm of a three-term arithmetic progression, contained in S. A result of Browkin, Divǐs and Schinzel implies that the size of a balanced subset of Fp is at least log2 p+1. In this paper we present an efficient algorithm which yields a balanced set of size (1 + o(1)) log2 p as p grows.
A generalized Davenport-Schinzel sequence is one over a finite alphabet that excludes subsequences isomorphic to a fixed forbidden subsequence. The fundamental problem in this area is bounding the maximum length of such sequences. Following Klazar, we let Expσ, nq be the maximum length of a sequence over an alphabet of size n excluding subsequences isomorphic to σ. It has been proved that for e...
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