Results 1  10
of
38
Shadows and isoperimetry under the sequencesubsequence relation
 Combinatorica
, 1997
"... One of the basic results in extremal set theory was discovered in [1] and rediscovered in [2]: For a given number of kelement subsets of an nset the shadow, that is, the set of (k 1)element subsets contained in at least one of the specified kelement subsets, is minimal, if the kelement subsets ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
One of the basic results in extremal set theory was discovered in [1] and rediscovered in [2]: For a given number of kelement subsets of an nset the shadow, that is, the set of (k 1)element subsets contained in at least one of the specified kelement subsets, is minimal, if the k
RELATIVE STANLEY–REISNER THEORY AND UPPER BOUND THEOREMS FOR MINKOWSKI SUMS
"... Abstract. In this paper we settle the longstanding question regarding the combinatorial complexity of Minkowski sums of polytopes: We give a tight upper bound for the number of faces of a Minkowski sum, including a characterization of the case of equality. We similarly give a (tight) upper bound th ..."
Abstract
 Add to MetaCart
theorem for mixed faces of Minkowski sums. These results have applications ranging from algebraic and tropical geometry to optimization. To establish these results, we develop relative Stanley–Reisner theory, a generalization of the algebraic theory of simplicial complexes inaugurated by Hochster, Reisner
Some Tradeoff Results for Polynomial Calculus [Extended Abstract]
"... We present sizespace tradeoffs for the polynomial calculus (PC) and polynomial calculus resolution (PCR) proof systems. These are the first true sizespace tradeoffs in any algebraic proof system, showing that size and space cannot be simultaneously optimized in these models. We achieve this by e ..."
Abstract

Cited by 9 (5 self)
 Add to MetaCart
We present sizespace tradeoffs for the polynomial calculus (PC) and polynomial calculus resolution (PCR) proof systems. These are the first true sizespace tradeoffs in any algebraic proof system, showing that size and space cannot be simultaneously optimized in these models. We achieve this by extending essentially all known sizespace tradeoffs for resolution to PC and PCR. As such, our results cover space complexity from constant all the way up to exponential and yield mostly superpolynomial or even exponential size blowups. Since the upper bounds in our tradeoffs hold for resolution, our work shows that there are formulas for which adding algebraic reasoning on top of resolution does not improve the tradeoff properties in any significant way. As byproducts of our analysis, we also obtain tradeoffs between space and degree in PC and PCR exactly matching analogous results for space versus width in resolution, and strengthen the resolution tradeoffs in [Beame, Beck, and Impagliazzo ’12] to apply also to kCNF formulas.
Advan es on Extremal Problems in Number Theory and Combinatori s
"... To keep an a
eptable size referen
es not listed at the end are given by the Bibliography of the re ent book [N ℄ and/or the page number of [N℄. 1. Starting with solutions of extremal problems for nite sets of numbers under divisibility
onstraints [with L.H. Kha
hatrian,
.f. [PS℄℄, then we des
ri ..."
Abstract
 Add to MetaCart
To keep an a
eptable size referen
es not listed at the end are given by the Bibliography of the re ent book [N ℄ and/or the page number of [N℄. 1. Starting with solutions of extremal problems for nite sets of numbers under divisibility
onstraints [with L.H. Kha
hatrian,
.f. [PS℄℄, then we des
A LocalGlobal Principle for VertexIsoperimetric Problems
, 1998
"... We consider the vertexisoperimetric problem for cartesian powers of a graph G. A total order on the vertex set of G is called isoperimetric if the boundary of sets of a given size k is minimum for any initial segment of , and the ball around any initial segment is again an initial segment of . We ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
are presented. We also discuss new relations between the vertexisoperimetric problems and Macaulay posets. 1 Introduction Discrete isoperimetric problems have been widely studied in the literature due to their theoretical interest and numerous applications (see [3] for a survey). Although all these problems
Isoperimetric Inequalities and the Width Parameters of Graphs?
"... Abstract. We relate the isoperimetric inequalities with many width parameters of graphs: treewidth, pathwidth and the carving width. Using these relations, we deduce 1. A lower bound for the treewidth in terms of girth and average degree 2. The exact values of the pathwidth and carving width of the ..."
Abstract
 Add to MetaCart
Abstract. We relate the isoperimetric inequalities with many width parameters of graphs: treewidth, pathwidth and the carving width. Using these relations, we deduce 1. A lower bound for the treewidth in terms of girth and average degree 2. The exact values of the pathwidth and carving width
A WileyInterscience Publication
 Digital Image Processing
"... New York • Chichester • Weinheim • Brisbane • Singapore • TorontoDesignations used by companies to distinguish their products are often claimed as trademarks. In all instances where John Wiley & Sons, Inc., is aware of a claim, the product names appear in initial capital or all capital letters. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
form or by any means, electronic or mechanical, including uploading, downloading, printing, decompiling, recording or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher. Requests to the Publisher
Editor of Heeding the Call for Change: Suggestions for Curricular Action
 The Mathematical Association of America. MAA Notes
, 1992
"... The MAA Notes and Reports Series, started in 1982, addresses a broad range of topics and themes of interest to all who are involved with undergraduate mathematics. The volumes in this series are readable, informative, and useful, and help the ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
The MAA Notes and Reports Series, started in 1982, addresses a broad range of topics and themes of interest to all who are involved with undergraduate mathematics. The volumes in this series are readable, informative, and useful, and help the
Results 1  10
of
38