Related papers: Counterexamples in Cake-Cutting
In the paper are proved theorems, which amplify the results of my paper "On the difference equation of Poincare type (Part 3)", Max-Plank-Institut fuer Mathematik, Bonn, Preprint Series, 2004, 09, 1-34.
In this paper a version of Knaster-Kuratowski-Mazurkiewicz theorem for products of simplices is formulated. Some corollaries for measure partition in the plane and cutting families of sets in the plane by lines are given.
We give a counterexample to the proof in the literature [K-Theory 25 (2002), 215-231] of the existence of linear representatives of higher Chow groups of number fields.
In [D.A. Fedoseev, V.O. Manturov, A sliceness criterion for odd free knots,arXiv:1707.04923], the authors proved a sliceness criterion for odd free knots: free knots with odd chords. In the present paper we give a similar criterion for…
Given a cake in form of a triangle and a box that fits the mirror image of the cake, how to cut the cake into a minimal number of pieces so that it can be put into the box? The cake has an icing, so that we are not allowed to put it into…
We study the problem of fairly allocating a divisible resource, also known as cake cutting, with an additional requirement that the shares that different agents receive should be sufficiently separated from one another. This captures, for…
The aim of these lecture notes, based on lectures given by the second author at the CIME school in Cetraro, is to illustrate a range of ideas surrounding higher Teichmuller spaces of Riemann surfaces with marked boundaries through explicit…
In this article we develop counterexamples to the Hasse principle using only techniques from undergraduate number theory and algebra. By keeping the technical prerequisites to a minimum, we hope to provide a path for nonspecialists to this…
We adapt a construction taken from `L. Motto Ros and B. Semmes, A new proof of a theorem of Jayne and Rogers, Real Anal. Exchange 35(1) (2009/2010), 195-204' in order to correct a mistake contained in the first part of the same paper. As a…
In this article we study the problem of fair division. In particular we study a notion introduced by J. Barbanel that generalizes super envy-free fair division. We give a new proof of his result. Our approach allows us to give an explicit…
This paper has been withdrawn by the author due to the presented idea is wrong.
In the recent past, the reduction-based and the model-based methods to prove cut elimination have converged, so that they now appear just as two sides of the same coin. This paper details some of the steps of this transformation.
Correction to Annals of Probability 28 (2000) 277--302 [doi:10.1214/aop/1019160120].
In this paper, we consider the classic fair division problem of allocating $m$ divisible items to $n$ agents with linear valuations over the items. We define novel notions of fair shares from the perspective of individual agents via the…
We introduce a generalized cake-cutting problem in which we seek to divide multiple cakes so that two players may get their most-preferred piece selections: a choice of one piece from each cake, allowing for the possibility of linked…
This paper is withdrawn. We found a mistake in Lemma 4.1
A counter example to the main result has been communicated to the author by Matei Toma.
We consider the problem of estimating counterfactual quantities when prior knowledge is available in the form of disjunctive statements. These include disjunction of conditions (e.g., "the patient is more than 60 years of age") as well as…
This paper has been withdrawn by the authors. It has been replaced by the papers: "Drawings of Planar Graphs with Few Slopes and Segments" (math/0606450) and "Graph Drawings with Few Slopes" (math/0606446).
Kotlarski's theorem (see H. Kotlarski. Bounded Induction and Satisfaction Classes. Mathematical Logic Quarterly, vol. 32, 31-34, 1986, P. 531--544.) formalized in $WKL_0$.