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Scott Is Always Simple [chapter]

Antonino Salibra
2012 Lecture Notes in Computer Science  
In this paper we give an outline of recent algebraic results concerning theories and models of the untyped 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.  ... 
doi:10.1007/978-3-642-32589-2_3 fatcat:jqadnhzb5jcudfucqdvxbirasa

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).  ... 

Connected chord diagrams and bridgeless maps [article]

Julien Courtiel, Karen Yeats, Noam Zeilberger
2017 arXiv   pre-print
Finally, 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  ...  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  ... 
arXiv:1611.04611v2 fatcat:pzdrvhbalnfq5pkcx3eefwvxcu

Connected Chord Diagrams and Bridgeless Maps

Julien Courtiel, Karen Yeats, Noam Zeilberger
2019 Electronic Journal of Combinatorics  
Finally, 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  ...  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  ... 
doi:10.37236/7400 fatcat:2oo6opmelrb3va4uxhneycchca

Applying Universal Algebra to Lambda Calculus

G. Manzonetto, A. Salibra
2008 Journal of Logic and Computation  
We show that the 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.  ... 
doi:10.1093/logcom/exn085 fatcat:muo26iplxbe2diepxtlnnutdxi

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.  ... 

Linear lambda terms as invariants of rooted trivalent maps

NOAM ZEILBERGER
2016 Journal of functional programming  
The main aim of the paper is to give a 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.  ... 
doi:10.1017/s095679681600023x fatcat:piay34hwofcabcwlinuic2qblu

Characters and composition factor multiplicities for the Lie superalgebra gl(m/n) [article]

J. Van der Jeugt, R.B. Zhang
1998 arXiv   pre-print
The multiplicities a_lambda,mu of 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.  ... 
arXiv:math/9811015v1 fatcat:kz3k36qs6vbalj5rqsxtm53sxa

Representations of Quivers Over F1 and Hall Algebras

M. Szczesny
2011 International mathematics research notices  
Thus 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 ≥ . . ..  ... 
doi:10.1093/imrn/rnr113 fatcat:uoo7hendxnhojfexs3lyr6obve

Representations of Quivers over F1 [article]

Matthew Szczesny
2011 arXiv   pre-print
Thus 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 ≥ . . ..  ... 
arXiv:1006.0912v3 fatcat:t6qgcfm24rblzanqvmtipua2qe

Indecomposable representations in symmetric b, c ghost systems via deformations of the Virasoro field

Michael Flohr, Julia Voelskow
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.  ... 
doi:10.1016/j.nuclphysb.2007.08.009 fatcat:uqrr3bvxkffbfj33sm5biosov4

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

Jianmin Chen, Yanan Lin, Shiquan Ruan
2013 arXiv   pre-print
We 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.  ... 
arXiv:1302.0504v1 fatcat:mssyxyl74bd5dfyykym3x4utue

Primitive set-theoretic solutions of the Yang-Baxter equation [article]

F. Cedo, E. Jespers, J. Okninski
2020 arXiv   pre-print
Introduction A fundamental open problem is to 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 : VVVV is a bijective linear  ...  Here R ij denotes the map VVVVVV acting as R on the (i, j) tensor factors and as the identity on the remaining factor.  ... 
arXiv:2003.01983v1 fatcat:4w4xa72wyrahxdpg4wdloq6zla

Symmetric Powers of Modular Representations for Groups with a Sylow Subgroup of Prime Order

Ian Hughes, Gregor Kemper
2001 Journal of Algebra  
We also obtain formulas which give generating functions encoding the decompositions of all symmetric powers of 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.  ... 
doi:10.1006/jabr.2000.8710 fatcat:jhce5h5nozcancdawotgoim4sq

The Excess Degree of a Polytope

Guillermo Pineda-Villavicencio, Julien Ugon, David Yost
2018 SIAM Journal on Discrete Mathematics  
it is 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 .  ... 
doi:10.1137/17m1131994 fatcat:kr6s5epxt5bcjcayvn2z6wdydu
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