103.24 Partitions, geometric progressions and a Putnam problem

2019 ◽  
Vol 103 (557) ◽  
pp. 337-343
Author(s):  
Shane Chern ◽  
Shiqiu Qiu
Keyword(s):  
Geometric Progressions

scholarly journals Multidimensional Multiplicative Combinatorial Properties of Dynamical Syndetic Sets

2021 ◽  
Author(s):  
Jiahao Qiu ◽  
Jianjie Zhao
Keyword(s):  
Normal Subgroup ◽  
Finite Index ◽  
Minimal System ◽  
Combinatorial Properties ◽  
Return Times ◽  
Residual Set ◽  
Closed Sets ◽  
Open Set ◽  
Geometric Progressions ◽  
Set Of Points

AbstractIn this paper, it is shown that for a minimal system (X, G), if H is a normal subgroup of G with finite index n, then X can be decomposed into n components of closed sets such that each component is minimal under H-action. Meanwhile, we prove that for a residual set of points in a minimal system with finitely many commuting homeomorphisms, the set of return times to any non-empty open set contains arbitrarily long geometric progressions in multidimension, extending a previous result by Glasscock, Koutsogiannis and Richter.

scholarly journals Metric discrepancy results for geometric progressions with small ratios

2018 ◽  
Vol 155 (2) ◽  
pp. 416-430 ◽  
Author(s):  
K. Fukuyama ◽  
S. Sakaguchi ◽  
O. Shimabe ◽  
T. Toyoda ◽  
M. Tscheckl
Keyword(s):  
Geometric Progressions

scholarly journals ON SEQUENCES WITHOUT GEOMETRIC PROGRESSIONS

Integers ◽  
2014 ◽  
Author(s):  
Melvyn B. Nathanson ◽  
Kevin O’Bryant
Keyword(s):  
Geometric Progressions

On Sequences Without k-Term Geometric Progressions

2014 ◽  
Vol 11 (2) ◽  
pp. 358-362
Author(s):  
Zhengwen Huang ◽  
Zehui Shao ◽  
Fei Deng ◽  
Xiaodong Xu
Keyword(s):  
Geometric Progressions

scholarly journals Polyploidy as a chromosomal component of stochastic noise: variable scalar multiples of the diploid chromosome complement in the invertebrate species Girardia schubarti from Brazil

2017 ◽  
Vol 77 (4) ◽  
pp. 745-751 ◽  
Author(s):  
E. G. F. Benya ◽  
A. M. Leal-Zanchet ◽  
J. Hauser
Keyword(s):  
Phenotypic Plasticity ◽  
Chromosome Complement ◽  
Dorsal Surface ◽  
Phenotypic Variance ◽  
Stochastic Noise ◽  
Body Width ◽  
Invertebrate Species ◽  
Geometric Progressions ◽  
Species Specific ◽  
Kinetics Of

Abstract Chromosome stoichiometry, a form of genetic plasticity, specifically refers to variation in the standard diploid genomic composition of an individual or species. In the present work, freshwater planarians (Girardia schubarti) were analyzed to recognize variations in chromosomal stoichiometry especially of complete ploidal change between specimens, within specimens and between cells within specimens and any relations they might have with selected components of phenotypic plasticity. Homoploid polyploids for the group reached rational scalar multiples (e.g. tetraploids) or irrational scalar multiples (e.g. triploids). Karyotypic mosaics emerged where individual cells presented polyploid multiples in arithmetic and geometric progressions. Ploidal multiplicity, a chromosomal component of stochastic noise, had positive phenotypic effects (increased dimensions) on morphologic criteria of body length, body width and dorsal surface reflecting a significant genotypic plasticity (GP) and robust phenotypic plasticity (PP). Variable but significant association of genotypic plasticity with robust phenotypic variance suggests kinetics of phenotypic homeostasis that is species-specific permitting phenotypic adaptability to environmental variables by means of GP. That association is diminished, deactivated or lost in more advanced and more complex organisms.

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