Filters








1,175 Hits in 4.8 sec

Partitions of Zn into arithmetic progressions

William Y.C. Chen, David G.L. Wang, Iris F. Zhang
2009 European journal of combinatorics (Print)  
We introduce the notion of arithmetic progression blocks or m-APblocks of Z n , which can be represented as sequences of the form Then we consider the problem of partitioning Z n into m-AP-blocks.  ...  We show that subject to a technical condition, the number of partitions of Z n into m-AP-blocks of a given type is independent of m, and is equal to the cyclic multinomial coefficient which has occurred  ...  This work was supported by the 973 Project, the PCSIRT Project of the Ministry of Education, the Ministry of Science and Technology, and the National Science Foundation of China.  ... 
doi:10.1016/j.ejc.2008.09.027 fatcat:ogsvo6c5fjht3mki3myn7yojze

Enumeration of monochromatic three term arithmetic progressions in two-colorings of cyclic groups [article]

Erik Sjöland
2014 arXiv   pre-print
One of the toughest problems in Ramsey theory is to determine the existence of monochromatic arithmetic progressions in groups whose elements have been colored.  ...  We study the harder problem to not only determine the existence of monochromatic arithmetic progressions, but to also count them.  ...  It follows that the minimum number of monochromatic arithmetic progression of length 3 in a 2-coloring of Z n is R(3, Z n , 2) = min x∈{−1,1} n {a,b,c} is an A.P. in Zn p(x a , x b , x c ).  ... 
arXiv:1408.1058v4 fatcat:nokdeyg6n5cc5aqmulhiuc7aoi

Discrepancy in modular arithmetic progressions [article]

Jacob Fox, Max Wenqiang Xu, Yunkun Zhou
2021 arXiv   pre-print
We asymptotically determine the logarithm of the discrepancy of arithmetic progressions in ℤ_n for all positive integer n.  ...  Celebrated theorems of Roth and of Matoušek and Spencer together show that the discrepancy of arithmetic progressions in the first n positive integers is Θ(n^1/4).  ...  Since each Z p α i i is partitioned into S (t) i for 0 ≤ t ≤ α i , their product is partitioned into Y r for r divides n, so Z n is partitioned into X r for r divides n.  ... 
arXiv:2104.03929v1 fatcat:jqjygnctubh5jfffuum26kc4ai

A new, fast, and efficient image codec based on set partitioning in hierarchical trees

A. Said, W.A. Pearlman
1996 IEEE transactions on circuits and systems for video technology (Print)  
Moreover, we present a new and different implementation based on set partitioning in hierarchical trees (SPIHT), which provides even better performance than our previously reported extension of EZW that  ...  In addition, the new coding and decoding procedures are extremely fast, and they can be made even faster, with only small loss in performance, by omitting entropy coding of the bit stream by arithmetic  ...  If C(z, J ) is significant, then it is partitioned into the four sets D ( k , I ) , with ( k , I ) E O(z, J ) .  ... 
doi:10.1109/76.499834 fatcat:mqpuwranwbe3ffpudaxsm4uhzi

Chebyshev-Vandermonde Systems

Lothar Reichel, Gerhard Opfer
1991 Mathematics of Computation  
Fast progressive algorithms for the solution of the Chebyshev-Vandermonde systems are described. These algorithms are closely related to methods recently presented by Higham.  ...  We present a progressive scheme for allocating distinct nodes zk on the boundary of the ellipse such that the Chebyshev-Vandermonde matrices obtained are reasonably well-conditioned.  ...  The product (3.13) is partitioned into subproducts, each of which contains 2 nodes zk that are distributed roughly like the first 2 nodes (1.9). Such a partitioning is described by [6, Lemma 2.3] .  ... 
doi:10.2307/2938712 fatcat:yucrxy53argqzhmulkqwsf73o4

Chebyshev-Vandermonde systems

Lothar Reichel, Gerhard Opfer
1991 Mathematics of Computation  
Fast progressive algorithms for the solution of the Chebyshev-Vandermonde systems are described. These algorithms are closely related to methods recently presented by Higham.  ...  We present a progressive scheme for allocating distinct nodes zk on the boundary of the ellipse such that the Chebyshev-Vandermonde matrices obtained are reasonably well-conditioned.  ...  The product (3.13) is partitioned into subproducts, each of which contains 2 nodes zk that are distributed roughly like the first 2 nodes (1.9). Such a partitioning is described by [6, Lemma 2.3] .  ... 
doi:10.1090/s0025-5718-1991-1094957-9 fatcat:rl4yxixhzfad5f6gccmavyfmqa

Author Index

1984 Mathematics of Computation  
Explicit Estimates for the Error Term in the Prime Number Theorem for Arithmetic Progressions. 265 McCurley, Kevin S. Explicit Estimates for 9(x;3,l) and i/>(x;3,Z). 287 Major, R. D.  ...  On the Sharpness of Certain Local Estimates for H Projections into Finite Element Spaces: Influence of a Reen-Difference Method for a Singular Boundary Value Problem of Second Order. 441 Weiss, Richard  ... 
doi:10.1090/s0025-5718-84-99808-9 fatcat:mzjl4g2yffbhljdgyokyx4opoa

Approaching optimality in spatially scalable video coding: From resampling and prediction to quantization and entropy coding

Jingning Han, Kenneth Rose
2013 2013 IEEE International Conference on Image Processing  
The internal range of the arithmetic coder is thus divided into (N − 1) subintervals, the i th of which has a length proportional toPi.  ...  INTRODUCTION Scalable video coding (SVC) consists of encoding a video sequence into a single bit-stream comprising multiple layers with progressively higher spatial, temporal, or quantization resolutions  ... 
doi:10.1109/icip.2013.6738370 dblp:conf/icip/HanR13 fatcat:s6kjn4asnjfobgmb3zplyuoqeq

On the reducibility of exact covering systems [article]

Ofir Schnabel
2015 arXiv   pre-print
As a consequence, if all moduli of an ECS A, are divisible by at most two distinct primes, then A is natural. That is, A can be formed by iteratively splitting the trivial ECS.  ...  These are ECS which are not a proper split of a coarser ECS. However, an ECS admiting a maximal modulus which is divisible by at most two distinct primes, primely splits a coarser ECS.  ...  Introduction An exact covering system (ECS) is a partition of Z into finitely many arithmetic progressions (1) A = {a s (n s )} k s=1 , where a(n) is the arithmetic progression a + Zn.  ... 
arXiv:1402.3957v2 fatcat:4pxkxxtaoja6thdsogf72y7jli

Sum-free sets, coloured graphs and designs

Anne Penfold Street, W. D. Wallis
1976 Journal of the Australian Mathematical Society  
Embedding of colourings is considered. Finally we illustrate a way of constructing colourings using block designs.  ...  Sum-free sets may be used to colour the edges of a complete graph in such a way as to avoid monochromatic triangles. We discuss the automorphism groups of such graphs.  ...  But T in arithmetic progression implies that TI -Ti is also in arithmetic progression; if | T) | = 5, then T) -T = S, which forces S f and hence Si to be in arithmetic progression.  ... 
doi:10.1017/s1446788700013343 fatcat:22f7ppsgsvckzp2rcsxvl756gm

On arithmetic partitions of Zn

Victor J.W. Guo, Jiang Zeng
2009 European journal of combinatorics (Print)  
Chen, Wang, and Zhang then studied the problem of partitioning _n into arithmetical progressions of a given type under some technical conditions.  ...  Generalizing a classical problem in enumerative combinatorics, Mansour and Sun counted the number of subsets of _n without certain separations.  ...  Acknowledgments We thank the referees for helpful comments on a previous version of this paper.  ... 
doi:10.1016/j.ejc.2008.11.009 fatcat:id5mdzyuqfgordepzycgftj6e4

Ramsey's theorem for $n$-dimensional arrays

R. L. Graham, B. L. Rothschild
1969 Bulletin of the American Mathematical Society  
Given integers k and r there exists an integer N(k t r) such that if n*zN(k, r) and the set I n is partitioned into r classes, then at least one class contains an arithmetic progression of length k.  ...  of the fe-parameter sets P k into r classes induces a partition of (k -1) -parameter sets Pfc-i to which we can apply the induction hypothesis.  ... 
doi:10.1090/s0002-9904-1969-12202-0 fatcat:qes7zrtcfrbkzelbiawmyy2e4a

The remarkable effectiveness of ergodic theory in number theory

Alexander Arbieto, Carlos Matheus, Carlos Moreira
2009 Ensaios matemáticos  
In this process, you get a partition of the integer numbers into k disjoint subsets.  ...  . , N } into r arithmetic progressions of ratio r, e.g., {1 ≤ n ≤ N | n ≡ a(mod r)}, for each a with 0 ≤ a ≤ r − 1.  ...  In this direction, in view of the geometrical interpretation of F (see remark 3.3.1), we look at the lattices Λ ∈ E intersecting the triangle ∆ c−,c+ into two points whose coordinates (w (1) 2 ∈ (c − ,  ... 
doi:10.21711/217504322009/em171 fatcat:wpa3cpqbmnfade45jd23kf4bai

Limestone doses affecting mineral contents in tropical grass forage

M. J. A. Armelin, O. Primavesi, A. C. Primavesi, M. Saiki
2005 Journal of Radioanalytical and Nuclear Chemistry  
The statistical analysis showed a negative linear correlation of Br, Co, Cr, Mn and Zn contents in forage with the limestone doses, while the uptake of Mg was affected in a positive way.  ...  by the use of limestone and fertilizer.  ...  Arithmetic mean values and concentration ranges of the elements Br, Co, Cr, Mg, Mn and Zn obtained in Brachiaria decumbens forage of 6 blocks are presented in Table 2 .  ... 
doi:10.1007/s10967-005-0670-4 fatcat:sn5rrbhilvfyxdgku5b63klx4y

On the Statistical Ensemble for the Theory of Helix-Coil Transition of Copolymeric DNA

Masa-aki Ozaki, Masahiro Tanaka, Youko Kawai, Ei Teramoto
1967 Progress of theoretical physics  
The treatment based on the Bernoulli ensemble leads to the arithmetic mean approximation for the statistical weight of bonded base pair and it fails to give the reasonable separate contributions of G-C  ...  Helix-coil transition of copolymeric DNA molecule is investigated hy calculating the partition functions averaged over two kinds of ensembles of 'random sequences of base pairs, namely, the Bernoulli ensemble  ...  If we average the partition functions over the Bernoulli ensemble, it leads to the arithmetic mean approximation.  ... 
doi:10.1143/ptp.38.9 fatcat:fbj6nxv3kvcqjkqs6kmis5tt3e
« Previous Showing results 1 — 15 out of 1,175 results