Peter Jipsen | Chapman University (original) (raw)

Papers by Peter Jipsen

Research paper thumbnail of P3-isomorphisms for graphs

Journal of Graph Theory, 1997

ABSTRACT The P3-graph of a finite simple graph G is the graph whose vertices are the 3-vertex pat... more ABSTRACT The P3-graph of a finite simple graph G is the graph whose vertices are the 3-vertex paths of G, with adjacency between two such paths whenever their union is a 4-vertex path or a 3-cycle. In this paper we show that connected fnite simple graphs G and H with isomorphic P3-graphs are either isomorphic or part of three exceptional families. We also characterize all isomorphisms between P3-graphs in terms of the original graphs. © 1997 John Wiley & Sons, Inc. J Graph Theory 26:35–51, 1997

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Research paper thumbnail of Small representations of the relation algebra ?n+1(1, 2, 3)

Algebra Universalis, 1995

ABSTRACT Applying combinatorial methods, we prove that the symmetric relation algebra ɛn+1(1, 2, ... more ABSTRACT Applying combinatorial methods, we prove that the symmetric relation algebra ɛn+1(1, 2, 3) ofn+1 atoms is finitely representable for alln ≳ 1, on at most (2+o(1))n2 elements asn → ∞. We explicitly construct a representation of size 4.5n2, for every n >1.

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Research paper thumbnail of Generating all finite modular lattices of a given size

Algebra universalis, 2015

ABSTRACT Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices tha... more ABSTRACT Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices that includes all distributive lattices. Heitzig and Reinhold developed an algorithm to enumerate, up to isomorphism, all finite lattices up to size 18. Here we adapt and improve this algorithm to construct and count modular lattices up to size 23, semimodular lattices up to size 22, and lattices of size 19. We also show that 2n−32^{n-3}2n−3 is a lower bound for the number of nonisomorphic modular lattices of size nnn.

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Research paper thumbnail of A Note on Complex Algebras of Semigroups

Lecture Notes in Computer Science, 2004

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Research paper thumbnail of Concurrent Kleene Algebra with Tests

Lecture Notes in Computer Science, 2014

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Research paper thumbnail of Categories of Algebraic Contexts Equivalent to Idempotent Semirings and Domain Semirings

Lecture Notes in Computer Science, 2012

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Research paper thumbnail of A Survey of Residuated Lattices

Developments in Mathematics, 2002

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Research paper thumbnail of Background Material

Relational Methods in Computer Science, 1997

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Research paper thumbnail of The Structure of the One-Generated Free Domain Semiring

Lecture Notes in Computer Science, 2008

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Research paper thumbnail of Blast 2013

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Research paper thumbnail of Conference on Ordered Algebraic Structures

... For more listing and sorting options, see the active list. Richard N. Ball Countably Indicate... more ... For more listing and sorting options, see the active list. Richard N. Ball Countably Indicated Uniform Convergence on Archimedean Lattice-Ordered Groups with Weak Unit Nikolaos Galatos Varieties of residuated lattices generated by positive universal classes. ...

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Research paper thumbnail of Computational general algebra on ten dollars a day

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Research paper thumbnail of Ultraproducts of Atomic Boolean Algebras

ABSTRACT Assuming the generalized continuum hypothesis the authors describe the saturated atomic ... more ABSTRACT Assuming the generalized continuum hypothesis the authors describe the saturated atomic Boolean algebra of an uncountable regular power as an ultraproduct of finite algebras or as an ultrapower of an infinite atomic Boolean algebra, always using a good ultrafilter. As a corollary they show that every infinite atomic Boolean algebra can be elementarily embedded in an ultrapower of finite Boolean algebras.

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Research paper thumbnail of Amalgamation in lattice varieties

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Research paper thumbnail of General results

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Research paper thumbnail of Nonmodular varieties

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Research paper thumbnail of Equational bases

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Research paper thumbnail of Preliminaries

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Research paper thumbnail of Modular varieties

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Research paper thumbnail of An orderly algorithm to enumerate finite (semi) modular lattices

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Research paper thumbnail of P3-isomorphisms for graphs

Journal of Graph Theory, 1997

ABSTRACT The P3-graph of a finite simple graph G is the graph whose vertices are the 3-vertex pat... more ABSTRACT The P3-graph of a finite simple graph G is the graph whose vertices are the 3-vertex paths of G, with adjacency between two such paths whenever their union is a 4-vertex path or a 3-cycle. In this paper we show that connected fnite simple graphs G and H with isomorphic P3-graphs are either isomorphic or part of three exceptional families. We also characterize all isomorphisms between P3-graphs in terms of the original graphs. © 1997 John Wiley & Sons, Inc. J Graph Theory 26:35–51, 1997

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Research paper thumbnail of Small representations of the relation algebra ?n+1(1, 2, 3)

Algebra Universalis, 1995

ABSTRACT Applying combinatorial methods, we prove that the symmetric relation algebra ɛn+1(1, 2, ... more ABSTRACT Applying combinatorial methods, we prove that the symmetric relation algebra ɛn+1(1, 2, 3) ofn+1 atoms is finitely representable for alln ≳ 1, on at most (2+o(1))n2 elements asn → ∞. We explicitly construct a representation of size 4.5n2, for every n >1.

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Research paper thumbnail of Generating all finite modular lattices of a given size

Algebra universalis, 2015

ABSTRACT Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices tha... more ABSTRACT Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices that includes all distributive lattices. Heitzig and Reinhold developed an algorithm to enumerate, up to isomorphism, all finite lattices up to size 18. Here we adapt and improve this algorithm to construct and count modular lattices up to size 23, semimodular lattices up to size 22, and lattices of size 19. We also show that 2n−32^{n-3}2n−3 is a lower bound for the number of nonisomorphic modular lattices of size nnn.

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Research paper thumbnail of A Note on Complex Algebras of Semigroups

Lecture Notes in Computer Science, 2004

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Research paper thumbnail of Concurrent Kleene Algebra with Tests

Lecture Notes in Computer Science, 2014

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Research paper thumbnail of Categories of Algebraic Contexts Equivalent to Idempotent Semirings and Domain Semirings

Lecture Notes in Computer Science, 2012

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Research paper thumbnail of A Survey of Residuated Lattices

Developments in Mathematics, 2002

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Research paper thumbnail of Background Material

Relational Methods in Computer Science, 1997

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Research paper thumbnail of The Structure of the One-Generated Free Domain Semiring

Lecture Notes in Computer Science, 2008

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Research paper thumbnail of Blast 2013

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Research paper thumbnail of Conference on Ordered Algebraic Structures

... For more listing and sorting options, see the active list. Richard N. Ball Countably Indicate... more ... For more listing and sorting options, see the active list. Richard N. Ball Countably Indicated Uniform Convergence on Archimedean Lattice-Ordered Groups with Weak Unit Nikolaos Galatos Varieties of residuated lattices generated by positive universal classes. ...

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Research paper thumbnail of Computational general algebra on ten dollars a day

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Research paper thumbnail of Ultraproducts of Atomic Boolean Algebras

ABSTRACT Assuming the generalized continuum hypothesis the authors describe the saturated atomic ... more ABSTRACT Assuming the generalized continuum hypothesis the authors describe the saturated atomic Boolean algebra of an uncountable regular power as an ultraproduct of finite algebras or as an ultrapower of an infinite atomic Boolean algebra, always using a good ultrafilter. As a corollary they show that every infinite atomic Boolean algebra can be elementarily embedded in an ultrapower of finite Boolean algebras.

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Research paper thumbnail of Amalgamation in lattice varieties

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Research paper thumbnail of General results

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Research paper thumbnail of Nonmodular varieties

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Research paper thumbnail of Equational bases

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Research paper thumbnail of Preliminaries

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Research paper thumbnail of Modular varieties

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Research paper thumbnail of An orderly algorithm to enumerate finite (semi) modular lattices

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