: ForasubsetS ofpositiveintegerslet (n, S)bethesetofpartitionsofnintosummands that are elements of S. For every (n, S), let Mn() be the number of parts, with multiplicity, that ...
We study the cover time of a random walk on the largest component of the random graph Gn,p. We determine its value up to a factor 1 + o(1) whenever np = c > 1, c = O(ln n). In ...
In this paper we consider some families of random Cantor sets on the line and investigate the question whether the condition that the sum of Hausdorff dimension is larger than one ...
For the only known universal best choice algorithm for partially ordered sets with known cardinality and unknown order (proposed by J. Preater) we improve the estimation of the lo...
Nicholas Georgiou, Malgorzata Kuchta, Michal Moray...
We study the cutoff phenomenon for generalized riffle shuffles where, at each step, the deck of cards is cut into a random number of packs of multinomial sizes which are then riffl...
It is now known that many properties of the objects in certain combinatorial structures are equivalent, in the sense that any object possessing any of the properties must of neces...