partition theorem
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2021 ◽  
Vol 70 (1) ◽  
Author(s):  
Arni S. R. Srinivasa Rao


2021 ◽  
Vol 344 (8) ◽  
pp. 112434
Author(s):  
Guantao Chen ◽  
Yanli Hao


10.37236/9941 ◽  
2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Jordan Mitchell Barrett

We further develop the theory of layered semigroups, as introduced by Farah, Hindman and McLeod, providing a general framework to prove Ramsey statements about such a semigroup $S$. By nonstandard and topological arguments, we show Ramsey statements on $S$ are implied by the existence of coherent sequences in $S$. This framework allows us to formalise and prove many results in Ramsey theory, including Gowers' $\mathrm{FIN}_k$ theorem, the Graham–Rothschild theorem, and Hindman's finite sums theorem. Other highlights include: a simple nonstandard proof of the Graham–Rothschild theorem for strong variable words; a nonstandard proof of Bergelson–Blass–Hindman's partition theorem for located variable words, using a result of Carlson, Hindman and Strauss; and a common generalisation of the latter result and Gowers' theorem, which can be proven in our framework.



Author(s):  
JIAYU KANG ◽  
RUNQIAO LI ◽  
ANDREW Y. Z. WANG

Abstract We find a new refinement of Fine’s partition theorem on partitions into distinct parts with the minimum part odd. As a consequence, we obtain two companion partition identities. Both analytic and combinatorial proofs are provided.



Author(s):  
Riccardo Aragona ◽  
Roberto Civino ◽  
Norberto Gavioli ◽  
Carlo Maria Scoppola

AbstractThe notion of rigid commutators is introduced to determine the sequence of the logarithms of the indices of a certain normalizer chain in the Sylow 2-subgroup of the symmetric group on $$2^n$$ 2 n letters. The terms of this sequence are proved to be those of the partial sums of the partitions of an integer into at least two distinct parts, that relates to a famous Euler’s partition theorem.





2019 ◽  
Vol 51 (1) ◽  
pp. 163-175
Author(s):  
John Murray
Keyword(s):  


2019 ◽  
Vol 49 (3) ◽  
pp. 555-565 ◽  
Author(s):  
Xinhua Xiong ◽  
William J. Keith
Keyword(s):  




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