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pro vyhledávání: '"Lang, Wolfdieter"'
Autor:
Lang, Wolfdieter
It is shown that each sequence giving the number of times a given day of the month falls on a certain day of the week for $400$ successive years of the Gregorian cycle can be composed of various pieces of various length of one of 4 sequences of lengt
Externí odkaz:
http://arxiv.org/abs/2311.13646
Autor:
Lang, Wolfdieter
Cantor gave in his fundamental article an elegant proof of the countability of real algebraic numbers based on a positive integer height, denoted by him as N, of integer and irreducible polynomials of given degree (denoted by him as n) with relative
Externí odkaz:
http://arxiv.org/abs/2307.10645
Autor:
Detlefs, Gary, Lang, Wolfdieter
The standard formula for the multi-section of the general linear three-term recurrence relation is simplified in terms of Chebyshev S-polynomials.
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
http://arxiv.org/abs/2304.12937
Autor:
Lang, Wolfdieter
The system of coaches by Hilton and Pedersen, the system of cyclic sequences of Schick, and Braendli-Bayne, related to diagonals in regular (2 n)-gons, and the system of modified modular doubling sequences elaborated in this paper are proved to be eq
Externí odkaz:
http://arxiv.org/abs/2008.04300
Autor:
Lang, Wolfdieter
It is shown that the unique representation of positive integers in terms of tribonacci numbers and the unique representation in terms of iterated A, B and C sequences defined from the tribonacci word are equivalent. Two auxiliary representations are
Externí odkaz:
http://arxiv.org/abs/1810.09787
Autor:
Lang, Wolfdieter
The exponential generating function of ordinary generating functions of diagonal sequences of general Sheffer triangles is computed by an application of Lagrange's theorem. For the special Jabotinsky type this is already known. An analogous computati
Externí odkaz:
http://arxiv.org/abs/1708.01421
Autor:
Lang, Wolfdieter
For finite sums of non-negative powers of arithmetic progressions the generating functions (ordinary and exponential ones) for given powers are computed. This leads to a two parameter generalization of Stirling and Eulerian numbers. A direct generali
Externí odkaz:
http://arxiv.org/abs/1707.04451
Autor:
Lang, Wolfdieter
Details for known solutions of some geometric and algebraic problems with the help of origami are presented: two theorems of Haga, the general cubic equation, especially the heptagon equation, doubling the cube as well as the trisection of angles $\a
Externí odkaz:
http://arxiv.org/abs/1409.4799
Autor:
Lang, Wolfdieter
Publikováno v:
Journal of Integer Sequences, Vol. 17 (2014) 14.11.7
Motivated by a recent work of Tr\"umper we consider the general Collatz word (up-down pattern) and the sequences following this pattern. The recurrences for the first and last sequence entries are given, obtained from repeated application of the gene
Externí odkaz:
http://arxiv.org/abs/1404.2710
Autor:
Lang, Wolfdieter
The normal field extension Q(rho(n)), with the algebraic number rho(n) = 2 cos(pi/n) for natural n, is related to ratios of the lengths between diagonals and the side of a regular n-gon. This has been considered in a paper by P. Steinbach. These rati
Externí odkaz:
http://arxiv.org/abs/1210.1018