6 papers
Cheeger-type inequalities for the second largest spectral gap from of the normalized Laplacian
Lies Beers, Raffaella Mulas, Jan Petr
We study the second largest spectral gap from of the normalized Laplacian of a graph, a quantity that appears in the literature in connection with random walks, expander graphs…
Ordered Ramsey and Turán numbers of alternating paths and their variants
Gaurav Kucheriya, Allan Lo, Jan Petr +2
An ordered graph is a graph whose vertex set is equipped with a total order. The ordered complete graph is the complete graph with vertex set equipped with the natura…
Intervals in Dyck paths and the wreath conjecture
Jan Petr, Pavel Turek
Let denote the total number of intervals of length across all Dyck paths of semilength such that each interval contains precisely falls. We give the formul…
The wreath matrix
Jan Petr, Pavel Turek
Let be positive integers and be the set of integers modulo . A conjecture of Baranyai from 1974 asks for a decomposition of -element subsets of $\m…
Towards odd-sunflowers: temperate families and lightnings
Jan Petr, Pavel Turek
Motivated by odd-sunflowers, introduced recently by Frankl, Pach, and P{á}lv{ö}lgyi, we initiate the study of temperate families: a family …
Reconstructing almost all of a point set in from randomly revealed pairwise distances
Douglas Barnes, Jan Petr, Julien Portier +2
Let be a set of points in , and suppose that the distance between each pair of points is revealed independently with probability . We study when this infor…