680 research outputs found
L'OSSERVATORIO REGIONALE DELLE TECNOLOGIE QUALE STRUMENTO PIANIFICATORIO PER LA'PPROPRIATA ALLOCAZIONE DELLE RISORSE
No full textAnother proof of free ribbon lemma
No full textFree ribbon lemma that every free sphere-link in the 4-sphere is a ribbon sphere-link is shown in an earlier paper by the author. In this paper, another proof of this lemma is given
A bound for Dickson's lemma
No full textWe consider a special case of Dickson's lemma: for any two functions on
the natural numbers there are two numbers such that both and
weakly increase on them, i.e., and . By a
combinatorial argument (due to the first author) a simple bound for such
is constructed. The combinatorics is based on the finite pigeon hole principle
and results in a descent lemma. From the descent lemma one can prove Dickson's
lemma, then guess what the bound might be, and verify it by an appropriate
proof. We also extract (via realizability) a bound from (a formalization of)
our proof of the descent lemma.
Keywords: Dickson's lemma, finite pigeon hole principle, program extraction
from proofs, non-computational quantifiers
Szemer\u27edi\u27s regularity lemma revisited
No full textSzemer\u27edi\u27s regularity lemma is a basic tool in graph theory, and also plays an important role in additive combinatorics, most notably in proving Szemer\\u27edi\u27s theorem on arithmetic progressions . In this note we revisit this lemma from the perspective of probability theory and information theory instead of graph theory, and observe a variant of this lemma which introduces a new parameter . This stronger version of the regularity lemma was iterated in a recent paper of the author to reprove
the analogous regularity lemma for hypergraphs
Congruence structure of planar semimodular lattices: The General Swing Lemma
No full textThe Swing Lemma of the second author describes how a congruence spreads from
a prime interval to another in a slim (having no sublattice), planar,
semimodular lattice. We generalize the Swing Lemma to planar semimodular
lattices
Iterative Robust Experiment Design for MIMO System Identification via the S-Lemma
No full textOptimal input design plays an important role in system identification for complex and multivariable systems. A known paradox in input design is that the optimal inputs depend on the true but unknown system. The aim of this paper is to design inputs for multivariable systems that are robust to all system variations within a given continuous uncertainty set. In the presented approach, the robust design problem is cast as an infinite-dimensional min-max optimization problem, and tackled via the S-lemma in an iterative approximation scheme. Experimental results from a multivariable motion system show that the algorithm enables significant robustness improvements.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Team Jan-Willem van Wingerde
On a lemma of Scarf
No full textThe aim of this note is to point out some combinatorial applications of a lemma of Scarf, proved first in the context of game theory. The usefulness of the lemma in combinatorics has already been demonstrated in a paper by the first author and R. Holzman (J. Combin. Theory Ser. B 73 (1) (1998) 1) where it was used to prove the existence of fractional kernels in digraphs not containing cyclic triangles. We indicate some links of the lemma to other combinatorial results, both in terms of its statement (being a relative of the Gale–Shapley theorem) and its proof (in which respect it is a kin of Sperner’s lemma). We use the lemma to prove a fractional version of the Gale–Shapley theorem for hypergraphs, which in turn directly implies an extension of this theorem to general (not necessarily bipartite) graphs due to Tan (J. Algorithms 12 (1) (1991) 154). We also prove the following result, related to a theorem of Sands et al. (J. Combin. Theory Ser. B 33 (3) (1982) 271): given a family of partial orders on the same ground set, there exists a system of weights on the vertices, which is (fractionally) independent in all orders, and each vertex is dominated by them in one of the orders
Abel's lemma on summation by parts and basic hypergeometric series
No full textAbstractBasic hypergeometric series identities are revisited systematically by means of Abel's lemma on summation by parts. Several new formulae and transformations are also established. The author is convinced that Abel's lemma on summation by parts is a natural choice in dealing with basic hypergeometric series
On Bergman's Diamond Lemma for Ring Theory
No full textThis expository and review paper deals with the Diamond Lemma for ring
theory, which is proved in the first section of G. M. Bergman, The Diamond
Lemma for Ring Theory, Advances in Mathematics, 29 (1978), pp. 178-218. No
originality of the present note is claimed on the part of the author, except
for some suggestions and figures. Throughout this paper, I shall mostly use
Bergman's expressions in his paper. In Remarks and Notes, the reader will find
some useful information on this topic.Comment: 15 page
An exploration of proofs of the Szemerédi regularity lemma
No full textabstract: This paper focuses on the Szemerédi regularity lemma, a result in the field of extremal graph theory. The lemma says that every graph can be partitioned into bounded equal parts such that most edges of the graph span these partitions, and these edges are distributed in a fairly uniform way. Definitions and notation will be established, leading to explorations of three proofs of the regularity lemma. These are a version of the original proof, a Pythagoras proof utilizing elemental geometry, and a proof utilizing concepts of spectral graph theory. This paper is intended to supplement the proofs with background information about the concepts utilized. Furthermore, it is the hope that this paper will serve as another resource for students and others to begin study of the regularity lemma
- …
