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Scott Is Always Simple
[chapter]

2012
*
Lecture Notes in Computer Science
*

In this paper we give an outline of recent algebraic results concerning theories and models of the untyped

doi:10.1007/978-3-642-32589-2_3
fatcat:jqadnhzb5jcudfucqdvxbirasa
*lambda*calculus. ... (ii) The class*V*DI of directly*indecomposable*members of*V*is a universal class. Proposition 6 . 6 All λ-models living in Scott, stable and strongly stable semantics are*simple*algebras.Proof. ... Then, the following conditions are equivalent:(i)*For*all A ∈*V*, the stalks A/θ I (I ∈ S maximal ideal) are directly*indecomposable*. ...##
###
Page 1215 of Mathematical Reviews Vol. , Issue 94c
[page]

1994
*
Mathematical Reviews
*

*For*the case 4 = 5, the authors prove that there exists an

*indecomposable*

*simple*triple system (

*v*, 3,5)

*for*all

*v*= 1,3 (mod 6),

*v*> 25. ... the existence of an

*indecomposable*

*simple*triple system (

*v*,3,A). ...

##
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Connected chord diagrams and bridgeless maps
[article]

2017
*
arXiv
*
pre-print

Finally, we explain how these results have a

arXiv:1611.04611v2
fatcat:pzdrvhbalnfq5pkcx3eefwvxcu
*simple*application to the combinatorics of*lambda*calculus, verifying the conjecture that a certain natural family of*lambda*terms is equinumerous with bridgeless ... We describe a bijection between these two classes, which naturally extends to*indecomposable*diagrams and general rooted maps. ... we explain how these results have a*simple*application to the combinatorics of*lambda*calculus, verifying the conjecture that a certain natural family of*lambda*terms is equinumerous with bridgeless maps ...##
###
Connected Chord Diagrams and Bridgeless Maps

2019
*
Electronic Journal of Combinatorics
*

Finally, we explain how these results have a

doi:10.37236/7400
fatcat:2oo6opmelrb3va4uxhneycchca
*simple*application to the combinatorics of*lambda*calculus, verifying the conjecture that a certain natural family of*lambda*terms is equinumerous with bridgeless ... We describe a bijection between these two classes, which naturally extends to*indecomposable*diagrams and general rooted maps. ... Therefore,*for*every vector w of the form (0,*v*1 , . . . ,*v*i−1 ,*v*i + 1,*v*i+1 . . . ,*v*n 2 , u 2 , . . . , u n 1 ), the set B w,S contains exactly*v*i + 1 diagrams of the form C 1 ⊕*k*C 2 , and zero ...##
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Applying Universal Algebra to Lambda Calculus

2008
*
Journal of Logic and Computation
*

We show that the

doi:10.1093/logcom/exn085
fatcat:muo26iplxbe2diepxtlnnutdxi
*indecomposable*semantics (i.e., the semantics of*lambda*calculus given in terms of models of*lambda*calculus, which are directly*indecomposable*as combinatory algebras) includes the continuous ... In fact the Stone representation theorem*for*Boolean algebras can be generalized to combinatory algebras and λ-abstraction algebras. ...*V*]). To help the reader to get familiar with the argument, we outline now Pierce's*construction*. ...##
###
Page 6922 of Mathematical Reviews Vol. , Issue 2001J
[page]

2001
*
Mathematical Reviews
*

Similarly, a Bush-type Hadamard matrix of order 36 is

*constructed*and used*for*the*construction*of an infinite family of designs with parameters*v*= 36(25" + 25"-'+---+514+1),*k*= 15(25)”", A= 6(25)”, and ... An example of a non-*simple*,*indecomposable*OA(18, 3, 3,2) is presented. E. ...##
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Linear lambda terms as invariants of rooted trivalent maps

2016
*
Journal of functional programming
*

The main aim of the paper is to give a

doi:10.1017/s095679681600023x
fatcat:piay34hwofcabcwlinuic2qblu
*simple*and conceptual account*for*the correspondence (originally described by Bodini, Gardy, and Jacquot) between α-equivalence classes of closed linear*lambda*terms ... We begin by recalling a familiar diagrammatic representation*for*linear*lambda*terms, while at the same time explaining how such diagrams may be read formally as a notation*for*endomorphisms of a reflexive ... I am grateful to Alain Giorgetti*for*introducing me to the idea of Tutte decomposition and*for*emphasizing its importance as a way of representing rooted maps. ...##
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Characters and composition factor multiplicities for the Lie superalgebra gl(m/n)
[article]

1998
*
arXiv
*
pre-print

The multiplicities a_lambda,mu of

arXiv:math/9811015v1
fatcat:kz3k36qs6vbalj5rqsxtm53sxa
*simple*modules L(mu) in the composition series of Kac modules*V*(*lambda*)*for*the Lie superalgebra gl(m/n) were described by Serganova, leading to her solution of the character ... In this Letter a*simple*rule is conjectured to find all nonzero a_lambda,mu*for*any given weight mu. ... Acknowledgements The authors would like to thank*V*. Serganova*for*her interest and*for*useful comments. J. ...##
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Representations of Quivers Over F1 and Hall Algebras

2011
*
International mathematics research notices
*

Thus

doi:10.1093/imrn/rnr113
fatcat:uoo7hendxnhojfexs3lyr6obve
*for*type A quivers, the functor () ⊗ F 1*K*is a bijection on*indecomposable*representations. Theorem 10. ... . , 0, 0, . . .)*for*partitions, which exhibits*lambda*as a non-increasing sequence of non-negative integers, i.e. λ 1 ≥ λ 2 ≥ . . .. ...##
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Representations of Quivers over F1
[article]

2011
*
arXiv
*
pre-print

Thus

arXiv:1006.0912v3
fatcat:t6qgcfm24rblzanqvmtipua2qe
*for*type A quivers, the functor () ⊗ F 1*K*is a bijection on*indecomposable*representations. Theorem 10. ... . , 0, 0, . . .)*for*partitions, which exhibits*lambda*as a non-increasing sequence of non-negative integers, i.e. λ 1 ≥ λ 2 ≥ . . .. ...##
###
Indecomposable representations in symmetric b, c ghost systems via deformations of the Virasoro field

2008
*
Nuclear Physics B
*

*For*

*lambda*=1, proven LCFT structures are made explicit through this deformation. ... In the other cases, the existence of Jordan cells is ruled out in favour of a novel kind of

*indecomposable*representations. ... Julia Voelskow would like to thank David Heilmann and Jan Schumacher

*for*their hospitality. She is very grateful to Nils Carqueville

*for*his careful reading of this document. ...

##
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Tilting objects in the stable category of vector bundles on the weighted projective line of type (2,2,2,2;λ)
[article]

2013
*
arXiv
*
pre-print

We

arXiv:1302.0504v1
fatcat:mssyxyl74bd5dfyykym3x4utue
*construct*a tilting object*for*the stable category of vector bundles on a weighted projective line X of type (2,2,2,2;\*lambda*), consisting of five rank two bundles and one rank three bundle, whose endomorphism ... The authors also thank Xiaowu Chen*for*his encouragement. ... Acknowledgements The authors would like to thank Helmut Lenzing*for*his lectures in Xiamen University in 2011 and his helpful suggestion. ...##
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Primitive set-theoretic solutions of the Yang-Baxter equation
[article]

2020
*
arXiv
*
pre-print

Introduction A fundamental open problem is to

arXiv:2003.01983v1
fatcat:4w4xa72wyrahxdpg4wdloq6zla
*construct*all solutions of the Yang-Baxter equation R 12 R 23 R 12 = R 23 R 12 R 23 , where*V*is a vector space and R :*V*⊗*V*→*V*⊗*V*is a bijective linear ... Here R ij denotes the map*V*⊗*V*⊗*V*→*V*⊗*V*⊗*V*acting as R on the (i, j) tensor factors and as the identity on the remaining factor. ...##
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Symmetric Powers of Modular Representations for Groups with a Sylow Subgroup of Prime Order

2001
*
Journal of Algebra
*

We also obtain formulas which give generating functions encoding the decompositions of all symmetric powers of

doi:10.1006/jabr.2000.8710
fatcat:jhce5h5nozcancdawotgoim4sq
*V*into*indecomposables*. ... Let*V*be a representation of a finite group G over a field of characteristic p. If p does not divide the group order, then Molien's formula gives the Hilbert series of the invariant ring. ... Moreover,*for*the projective*indecomposable*KG-modules*V*ϕ we have dim*V*G ϕ = δ 1 ϕ since*V*ϕ has a*simple*socle with Brauer character ϕ. Proposition 2.3. ...##
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The Excess Degree of a Polytope

2018
*
SIAM Journal on Discrete Mathematics
*

it is

doi:10.1137/17m1131994
fatcat:kr6s5epxt5bcjcayvn2z6wdydu
*indecomposable*. ... As usual, the (Minkowski) sum of two polytopes Q + R is defined to be \{ x + y : x \in Q, y \in R\} , and a polytope P is said to be homothetic to a polytope Q if Q = \*lambda*P + t*for*\*lambda*> 0 and ... Note that every vertex in*K*is*simple*in F 3 , and thus,*v*must be*simple*in F 3 . ...
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