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Ramsey numbers for trees II

Zhi-Hong Sun (2021)

Czechoslovak Mathematical Journal

Let r ( G 1 , G 2 ) be the Ramsey number of the two graphs G 1 and G 2 . For n 1 n 2 1 let S ( n 1 , n 2 ) be the double star given by V ( S ( n 1 , n 2 ) ) = { v 0 , v 1 , ... , v n 1 , w 0 , w 1 , ... , w n 2 } and E ( S ( n 1 , n 2 ) ) = { v 0 v 1 , ... , v 0 v n 1 , v 0 w 0 , w 0 w 1 , ... , w 0 w n 2 } . We determine r ( K 1 , m - 1 , S ( n 1 , ...

Ramsey-type theorems

Gavalec, Martin, Vojtáš, Peter (1980)

Abstracta. 8th Winter School on Abstract Analysis

Random walks on the affine group of local fields and of homogeneous trees

Donald I. Cartwright, Vadim A. Kaimanovich, Wolfgang Woess (1994)

Annales de l'institut Fourier

The affine group of a local field acts on the tree 𝕋 ( 𝔉 ) (the Bruhat-Tits building of GL ( 2 , 𝔉 ) ) with a fixed point in the space of ends 𝕋 ( F ) . More generally, we define the affine group Aff ( 𝔉 ) of any homogeneous tree 𝕋 as the group of all automorphisms of 𝕋 with a common fixed point in 𝕋 , and establish main asymptotic properties of random products in Aff ( 𝔉 ) : (1) law of large numbers and central limit theorem; (2) convergence to 𝕋 and solvability of the Dirichlet problem at infinity; (3) identification of the Poisson boundary...

Rank decomposition in zero pattern matrix algebras

Harm Bart, Torsten Ehrhardt, Bernd Silbermann (2016)

Czechoslovak Mathematical Journal

For a block upper triangular matrix, a necessary and sufficient condition has been given to let it be the sum of block upper rectangular matrices satisfying certain rank constraints; see H. Bart, A. P. M. Wagelmans (2000). The proof involves elements from integer programming and employs Farkas' lemma. The algebra of block upper triangular matrices can be viewed as a matrix algebra determined by a pattern of zeros. The present note is concerned with the question whether the decomposition result referred...

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