ICTP Analysis Seminar - Wednesday 22 November, at 14:00 - VENUE: Luigi Stasi seminar room

[ICTP Math Section]

Analysis Seminar *"On the number of lower sets with fixed cardinality"*


Wednesday 22 Nov 2023, at 14:00


VENUE: Leonardo Building - Luigi Stasi Seminar Room


Speaker: Kristina Oganesyan (Universitat Autonoma de Barcelona)


Abstract: We call a set S in N^d, d>1, a lower set if for any x in S all 
the points in N^d with each coordinate being less or equal to that of x 
also belong to S. Equivalently, one can think of a d-dimensional lower 
set as of a union of unit cubes such that in each direction any cube 
leans either on another one or on the coordinate hyperplane.

We will be interested in estimating the number p_d(n) of d-dimensional 
lower sets of cardinality n. The two-sided inequality n^(1-1/d)<log 
p_d(n)< C(d)n^(1-1/d) is known to be true whenever n is large enough in 
terms of d. We show that if d is sufficiently small with respect to n, 
then C does not depend on d, which means that log p_d(n) is up to an 
absolute constant equal to n^(1-1/d).

/https://indico.ictp.it/event/10575/

-- 
Koutou Mabilo
ICTP Mathematics Group
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