Seminar for Combinatorics, Geometry, Algebra and Topology
Seminar Kombinatorika, Geometrija, Topologija, Algebra (KGTA)
PLAN RADA ZA DECEMBAR 2018:
UTORAK, 11.12.2018. od 14:00 do 16:00, Matematički fakultet, sala 844 (5. sprat)
Erika Berenice Roldán Roa, The Ohio State University
ASYMPTOTIC BEHAVIOR OF THE HOMOLOGY OF RANDOM POLYOMINOES
In this talk we study the rate of growth of the expectation of the number of holes (the rank of the first homology group) in a polyomino with uniform and percolation distributions. We prove the existence of linear bounds for the expected number of holes of a polyomino with respect to both the uniform and percolation distributions. Furthermore, we exhibit particular constants for the upper and lower bounds in the uniform distribution case. This results can be extend, using the same techniques, to other polyforms and higher dimensions.
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