In all questions that involve random variables which may assume a continuous range of values, we must carefully specify the probability distribution involved. This is often more delicate than in the discrete case. Here, it suffices to say that if 0<a<b<1, a "random number" between 0 and...
From my perspective, the question of whether quantum computation is possible is among the most important open scientific questions of our time. I hold the view that building scalable quantum computers—and even achieving some early milestones on the path to quantum computing—is impossible. Given th...
Then there exists a choice of splitting as in (3.1) (so F s (S s T)⊂N s for all s), such that x=o is the center of this splitting and none of the points y 1,…,y r−1 lies on the hyperplane T⊕N 2⊕N 3⊕⋯. Proof Let G be the automorphism group of X and P...
Given a partition\lambdaofnwith at mostNparts, themonomial symmetric polynomialsism_{\lambda }(x_1,\ldots ,x_N):=\sum _{\alpha }x_1^{\alpha _1}\cdots x_N^{\alpha _N}, where the sum is over all distinct permutations\alphaof the parts of\lambda. For example,m_{(2,1)}(x_...
For quick questions, please ask me after class. The class policy is to not answer by email any math questions related to the class, due to time constraints and also that emails are not a great medium for such Q&As (ask them during office hours instead). Clarification questions (about ...
In this paper, we deal with algorithmic questions that arise if nothing is known about the breaking points, i.e., we assume random fragmentation. Testing for random weights is algorithmically far more complex than the digestion method, because the cutting places are not known in advance, and ...
The machinery developed in this paper turns out to have application to other questions within permutation group theory. Indeed, it is possible to use variants of the results given in Sect. 3 to recover, and strengthen, classical results concerning multiply transitive groups due to Manning [13–15...
denotes a linear code of lengthn, dimensionkand distancedover the field. We will write [n,k,d] instead ofwhen the particular choice of the field is not important. Letbe an [n,k,d] code and,. We say thatSis an information set if the restriction. ...
6 Open questions Question 1 Is there a constant k, which does not depend on n, such that in an optimal distribution of Pn◻Pn no pebble can be moved to the distance-k neighborhood of its initial location? Question 2 If the answer for Question 1 is yes, then how small can be k?
In order to answer these questions we exploit a close connection between the Orlik–Terao algebra and the broken circuit algebra associated with the arrangement which was in particular studied in [29]: for any choice of ordering of the hyperplanes, the latter one is a deformation of the former...