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Incidence algebra The members of the incidence algebra are the functionss f assigning to each interval [a, b] a scalar f(a, b). Any member of an incidence algebra that assigns the same value to any two intervals that are isomorphic to each other as posets is a member of the reduced incidence algebra. Incidence algebras of locally finite posets were treated in a number of papers of Gian-Carlo Rota beginning in 1964, and by many later combinatorialists. www.brainyencyclopedia.com /encyclopedia/i/in/incidence_algebra.html   (605 words)

Heyting algebra -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-11-06) Heyting algebras arise as models of (Click link for more info and facts about intuitionistic logic) intuitionistic logic, a logic in which the (Click link for more info and facts about law of excluded middle) law of excluded middle does not in general hold. A bounded lattice H is a Heyting algebra (Click link for more info and facts about iff) iff all mappings are the lower adjoint of a monotone (Click link for more info and facts about Galois connection) Galois connection. In this case, the element is the (The region that is inside of something) interior of the union of and B, where denotes the complement of the open set A. www.absoluteastronomy.com /encyclopedia/h/he/heyting_algebra.htm   (1018 words)

Matrices Help Relationships Because the immensely powerful subject linear algebra, spreadsheet mathematics for those who don't know what linear algebra is, can now be brought to bear on the study of relationships. To see why, set up the incidence matrix for the relationship between faces and edges of a deltahedron by "is a face containing the edge". Hence the sum of all the ones in the incidence matrix is 3F, where F is the number of faces in the given deltahedron. www.cut-the-knot.com /blue/relation.shtml   (738 words)

Order theory - Wikipedia, the free encyclopedia Finally, various structures in mathematics combine orders with even more algebraic operations, as in the case of quantales, that allow for the definition of an addition operation. Locally finite posets give rise to incidence algebras which in turn can be used to define the Euler characteristic of finite bounded posets. An example is given by the correspondence between Boolean algebras and Boolean rings. en.wikipedia.org /wiki/Order_theory   (4054 words)

Clifford's Chains, Miquel's points, Morley, Algebra, Incidence Morley's research started with the incidence results of Steiner, Kantor and Clifford that in themselves are among the most intriguing in geometry. He applied his method to circumscribed as well inscribed circles, he studied incidence of their centers as well as their intersection points with other circles, he moved from circles to higher order curves. Yes, with all the geometric context of his theory, Morley's method is purely algebraic, founded on the theory of complex numbers. www.cut-the-knot.org /triangle/Morley/CenterCircle.shtml   (1256 words)

Citations: Introduction to non-associative algebra - Schafer (ResearchIndex)   (Site not responding. Last check: 2007-11-06) Fix C to be the split Cayley algebra endowed with hyperbolic norm form n and canonical involution denoted by. Thus, the dimension obtained by a particular two generator construction of an alternative algebra should remain unchanged when the identities are replaced by the associative law. Algebraic framework In this section we formulate quantum spin chains in a general algebraic framework and define the sequence of charges with Catalan tree pattern. citeseer.ist.psu.edu /context/171730/0   (2054 words)

Glossary of order theory   (Site not responding. Last check: 2007-11-06) A Boolean algebra is a distributive lattice with least element 0 and greatest element 1, in which every element x has a complement ¬x, such that x ^ ¬x = 0 and x v ¬x = 1. A Heyting algebra that is a complete lattice is called a complete Heyting algebra. The incidence algebra of a poset is the associative algebra of all scalar-valued functions on intervals, with addition and scalar multiplication defined pointwise, and multiplication defined as a certain convoluation; see incidence algebra for the details. www.free-download-soft.com /info/startup-manager.html   (2564 words)

Invariant Discretization Methods for n-Dimensional Nonlinear Reactive Transport Models   (Site not responding. Last check: 2007-11-06) We are constructing a new class of combinatorial methods, based on symmetry-invariant re-mapping and coordinate-free incidence algebra representations of the geometric face lattices of grid complexes, which preserve the invariant physical symmetries of the physical problem domain. This new class of discretization methods will faithfully represent and preserve both the fundamental algebraic and geometric symmetries of the continuum mathematical models, which are realized by a fundamental set of discrete Lie groups that approximate the continuous Lie groups associated with the system of ODEs that solve the physical domain PDEs. We have begun the construction of a novel lattice representation of the incidence graphs of grid data structures for mesh data models. www.emsl.pnl.gov /docs/tms/annual_report1999/1619b-2c.html   (1210 words)

Koen De Naeghel's Home Page   (Site not responding. Last check: 2007-11-06) On incidence between strata of the Hilbert scheme of points on P^2, submitted. "On the incidence between strata of the Hilbert scheme of points on the projective plane", Workshop noncommutative algebra Warwick, July 15, 2004. "On the incidence between strata of the Hilbert scheme of points on the projective plane", University of Washington Seattle, August 18, 2004. alpha.uhasselt.be /~lucp1324   (831 words)

Pure   (Site not responding. Last check: 2007-11-06) The principals of computer vision in geometric algebra, how estimation can be done using geometric algebra and the presentation of the invariant theory for the projective reconstruction of shape and motion are the subject of this part. In the part of quantum and neural computing the book shows the use of geometric algebra for analyzing the quantum states and quantum logic (based on nuclear magnetic resonance), the generalization of neural networks (using complex, hyperbolic and dual numbers) and the construction of wavelets from multivectors (a generalization of the quaternion wavelet concept). The software available for doing computer-aided calculations in geometric algebra represents the object of the part which will spur the further development of urgently needed software to do symbolic calculations in geometric algebra. www.library.tuiasi.ro /ipm/vol13no34/pure.html   (1071 words)

Publications and other projects   (Site not responding. Last check: 2007-11-06) Abstract: The N-variable Hopf algebra introduced by Brouder, Fabretti, and Krattenaler (BFK) in the context of non-commutative Lagrange inversion can be identified with the inverse of the incidence algebra of N-colored interval partitions. As in the case of the Faa di Bruno Hopf algebra, there is an analogue of the Zimmermann cancellation formula. First, we show that the vacuum vector is cyclic and separating for the algebra generated by such a process. math.ucr.edu /~manshel/pop.html   (1677 words)

Citebase - Finitary Algebraic Superspace Authors: Zapatrin, R. An algebraic scheme is suggested in which discretized spacetime turns out to be a quantum observable. An algebraic quantization procedure for discretized spacetime models is suggested based on the duality between finitary substitutes and their incidence algebras. The suggested scenario is along the lines of a similar algebraization and quantum interpretation of finitary topological spaces due to Zapatrin and this author. citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:gr-qc/9704062   (1165 words)

On incidence algebras associated with regular cell decomposition of S n (ResearchIndex)   (Site not responding. Last check: 2007-11-06) On incidence algebras associated with regular cell decomposition of S n We obtain the global dimension of such algebras and prove that they are Koszul algebras. The Preprojective Algebra of a Quiver - Ringel (1997) citeseer.ist.psu.edu /106402.html   (388 words)

A procedure for generating incidence matrices Finally, as an advanced example, we show how to compute an incidence matrix from a list of edges in a network. The directed edges can be given as a list of pairs [i,j] where i is the beginning node of the edge and j is the ending node. Thus, from a list of these pairs, we should be able to generate the incidence matrix. www.math.okstate.edu /~wrightd/5593/maple-intro/node19.html   (266 words)

WAM Abstracts We consider the algebraic implications that certain properties have on zero divisors in Jacobson radical rings and explore related properties such as topological nilpotents in Banach algebras. In particular, the Mikusi\\\'{n}ski algebra M, the collection of all continuous, complex valued functions defined on [0, \infty) with the convolution operation (f*g)(t)=\int_0^t f(t-\tau)g(\tau) d\tau, is considered. It is known that J(M)= M, and the absence of nonzero divisors of zero in M is equivalent to the Theorem of Titchmarsh from analysis. www.math.fau.edu /weekend-algebra/abstracts.html   (2230 words)

s15zeng   (Site not responding. Last check: 2007-11-06) The algebraic setting for the "Möbius inversion" is the "incidence algebra". We survey a general theory of incidence algebras, and indicate several applications. The paper has been finally published as the book "Möbius functions, incidence algebras and power series representations", Lecture Notes in Mathematics, 1202. www.maths.tcd.ie /EMIS/journals/SLC/opapers/s15duer.html   (53 words)

[No title] It was also Hadwiger who observed in 1960 that $\chi$ can be extended to a linear functional on the vector space consisting of the characteristic functions of convex bodies. Next he proposes the possibilities of proving many corollaries of the Euler-type relation by using the notion of an incidence algebra, due to G.-C. Rota. For example, the equality (phi {sup}) {sup}= phi is proved as a corollary of the Euler relation through the language of incidence algebra. www.math.niu.edu /~rusin/known-math/96/euler.fmla   (1221 words)

Hopf Algebras and Edge-Labeled Posets (ResearchIndex)   (Site not responding. Last check: 2007-11-06) This is a common generalization of a generating function for the flag f-vector defined by Ehrenborg and of a symmetric function associated to certain edge-labeled posets which arose in the theory of Schubert polynomials. We show this construction gives a Hopf morphism from an incidence Hopf algebra of edge-labeled posets to the Hopf algebra... 16 Antipodes and incidence coalgebras (context) - Schmitt - 1987 ACM citeseer.ist.psu.edu /554143.html   (340 words)

Papers Available   (Site not responding. Last check: 2007-11-06) We introduce and study a family of operators which act in the group algebra of a Weyl group W and provide a multi-parameter solution to the quantum Yang-Baxter equations of the corresponding type. We introduce a new multiplication in the incidence algebra of a partially ordered set, and study the resulting algebra. Log-concave and unimodal sequences arise often in combinatorics, algebra, geometry and computer science, as well as in probability and statistics where these concepts were first defined and studied. www.mat.uniroma2.it /~brenti/papers.htm   (2622 words)

Technische Universiteit Eindhoven, Faculteit Wiskunde en Informatica, Vakgroep Discrete Wiskunde With G. Ivanyos, A. Kuronya and L. Rónyai we studied the Levi decomposition of a Lie algebra in characteristic zero. The conjecture is based on a surprising patern in the decomposition of the tensor powers of the adjoint representation of these groups. As a consequence of this characterisation the automorphism group and the algebra of derivations of these Lie algebras could be determined. www.win.tue.nl /math/eidma/jaarverslagen/verslag95/node9.html   (1072 words)

m133 This course treats the elementary theory of affine and projective planes, finite geometries, Euclidean and Non-Euclidean geometries, groups of transformations and other algebraic structures related to geometry. Cyclic and dihedral groups, conjugate subgroups, Leonardo's theorem, regular polygons and their symmetries and similarities. Background material from solid geometry and vector algebra, planes, incidence geometry of the sphere, the spherical triangle inequality, isometries of the sphere, Euler's formula, spherical triangles, congruence theorems and trigonometry, finite rotation groups and isometry groups of the sphere. math.ucr.edu /home/UndergradInfo/pages/m133   (263 words)

Abstracts of papers by Peter J. Cameron A classification of incidence matrices is considered for which conditions of symmetry by transposition, having no repeated rows/columns, or identification by permutation of rows/columns are imposed. In the case where M is the signed vertex-edge incidence matrix of a graph Gamma over the ring of integers, the orbital Tutte polynomial specialises to count orbits of G on proper colourings of Gamma or on nowhere-zero flows or tensions on Gamma with values in an abelian group A. An independence algebra is an algebra A in which the subalgebras satisfy the exchange axiom, and any map from a basis of A into A extends to an endomorphism. www.maths.qmw.ac.uk /~pjc/abstracts.html   (8219 words)

Geometry-Algebra-Singularities-Combinatorics Seminar Talk Abstract: Resolutions of spaces that are prescribed by the combinatorial incidence structure of natural stratifications have appeared at many places. We present an abstract framework for the incidence combinatorics of strata in these situations: Inspired by the combinatorial notions used by DeConcini and Procesi, we define building sets and nested sets for arbitrary meet-semilattices on purely order-theoretic level. We define combinatorial blowups of meet-semilattices and show that a sequence of such combinatorial blowups, prescribed by a building set, transforms the original meet-semilattice into the face poset of the simplicial complex of nested sets. www.math.neu.edu /GASC/GAS/feichtner.html   (193 words)

[No title] L.B. Beasley and L. Cummings; Permanent semigroups, Linear and Multilinear Algebra 5 (1978), 297-302. L.J. Cummings and W.D. Wallis; A transversal algorithm for regular square incidence matrices, Eight Southeastern Conference on Combinatorics, Graph Theory and Computing, March 1977, Louisiana State University, 213-226. Cummings; Comma-free codes and incidence algebras (invited address), Proceedings of the fourth Australian Conference on Combinatorical Mathematics, Adelaide 1975, Lecture Notes in Mathematics, Vol. www.math.uwaterloo.ca /~ljcummin/info/cv.txt   (2113 words)

Euler characteristic   (Site not responding. Last check: 2007-11-06) A poset is "bounded" if it has smallest and largest elements, which let us call 0 and 1. The Euler characteristic of such a poset is μ(0,1), where μ is the Möbius function in that poset's incidence algebra. Shiraz, that "they asked a wise man, saying: Of the many celebrated call none azad, or free, excepting the cypress, which bears no appropriate produce, and appointed season.html">season, during the continuance of withered; to neither of which states is the cypress exposed, being independents. www.wordlookup.net /eu/euler-characteristic.html   (551 words)

[No title]   (Site not responding. Last check: 2007-11-06) ** Abstract We will recall/define the notion of the incidence algebra of a poset. We will consider the incidence algebra of the lattice of finite modules over a ring, as well as some related algebras. To avoid unpleasent technicalities, we will ilustrate our methods on the modest example of O being a finite field. www.math.technion.ac.il /~techm/20030610161020030610bad   (84 words)

2003 Incidence Algebra of a Triangular Category and Calculus of Fractions, (with G.Schwab) Proceedings of the Conference on Algebra “Babes- Bolyai” University of Cluj- Proceedings of the Algebra Conference University of Brasov, 1989, 127-132. science.utep.edu /faculty/papers/Emil_Daniel_Schwab.html   (474 words)

AGACSE 2001 Abstracts - Bayro   (Site not responding. Last check: 2007-11-06) This paper presents algebra of incidence using the framework of the n-dimensional affine plane. As opposite to former approaches we show that in this framework we can conciliate a degenerated sub-algebra for rigid motion computations and a geometric sub-algebra for incidence algebra operations. Interesting applications of kinematics computations, reaching and con guration checking are presented. www.mrao.cam.ac.uk /agacse2001/Abstracts/Bayro2.htm   (64 words)

Talks EIDMA Minicourse on "New Approaches to Computing Finite Groups Invariants", April 15-19, 2002, Free University of Brussels. Magma workshop on Group Theory and Algebraic Geometry, University of Warwick, August 22-26, 2005. Incidence geometry, finite group theory and computational algebra. cso.ulb.ac.be /~dleemans/talks.html   (218 words)

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