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A determinant formula from random walks

Hery Randriamaro (2023)

Archivum Mathematicum

One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows to compute...

A family of 4-designs on 26 points

Dragan M. Acketa, Vojislav Mudrinski (1996)

Commentationes Mathematicae Universitatis Carolinae

Using the Kramer-Mesner method, 4 - ( 26 , 6 , λ ) designs with P S L ( 2 , 25 ) as a group of automorphisms and with λ in the set { 30 , 51 , 60 , 81 , 90 , 111 } are constructed. The search uses specific partitioning of columns of the orbit incidence matrix, related to so-called “quasi-designs”. Actions of groups P S L ( 2 , 25 ) , P G L ( 2 , 25 ) and twisted P G L ( 2 , 25 ) are being compared. It is shown that there exist 4 - ( 26 , 6 , λ ) designs with P G L ( 2 , 25 ) , respectively twisted P G L ( 2 , 25 ) as a group of automorphisms and with λ in the set { 51 , 60 , 81 , 90 , 111 } . With λ in the set { 60 , 81 } , there exist designs which possess all three considered groups...

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