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Solutions of modular bootstrap constraints from quantum codes [article]

Anatoly Dymarsky, Alfred Shapere
2020 arXiv   pre-print
This relation reduces modular invariance of the 2d CFT partition function to simple algebraic relations at the level of a multivariate polynomial characterizing the corresponding code.  ...  Here we report a way to assign to a particular family of quantum error correcting codes a family of "code CFTs" -- a subset in the space of Narain CFTs.  ...  There are also many polynomials obeying the standard symmetries and constraints of the enumerator polynomial, which are nevertheless not enumerator polynomials of any actual code.  ... 
arXiv:2009.01236v1 fatcat:6mic6l6225cd7j6huvywz4j6ni

Page 1702 of Mathematical Reviews Vol. , Issue 88d [page]

1988 Mathematical Reviews  
Suppose that lattice points p and q lie on the same side of this line.  ...  rational operations on languages to enumeration.  ... 

Page 6688 of Mathematical Reviews Vol. , Issue 88m [page]

1988 Mathematical Reviews  
A method for the enumeration of clusters G on a d-dimensional hypercubic lattice is presented.  ...  Brooks (1-PA-P); Meir, Yigal (IL-TLAV-P) Recursive enumeration of clusters in general dimension on hypercubic lattices. Phys. Rev. A (3) 36 (1987), no. 4, 1840-1848.  ... 

On-node lattices construction using partial Gauss–Hermite quadrature for the lattice Boltzmann method

Huanfeng Ye, Zecheng Gan, Bo Kuang, Yanhua Yang
2019 Chinese Physics B  
The search reveals a surprising abundance of available lattices.  ...  A concise theoretical framework, the partial Gauss-Hermite quadrature (pGHQ), is established for constructing on-node lattices of the lattice Boltzmann (LB) method under a Cartesian coordinate system.  ...  The detailed procedures of searching local optimal lattices on [−m, m] for u n ED discretization are: a) Set up q, start up with theoretically smallest number q = n + 1 b) Enumerate all possible q-point  ... 
doi:10.1088/1674-1056/28/5/054702 fatcat:a75lmju5mnem5nmgn3mlyh2qqy

Page 6278 of Mathematical Reviews Vol. , Issue 89K [page]

1989 Mathematical Reviews  
This paper pro- vides an enumeration and properties of subalgebras of AP(2, 3) of codimension 1.  ...  From the text: “It is well known that multidimensional quantum- mechanical models with polynomial potentials play an important role in many fields of quantum physics.  ... 

Extensions of partial cyclic orders and consecutive coordinate polytopes

Arvind Ayyer, Matthieu Josuat-Vergès, Sanjay Ramassamy
2020 Annales Henri Lebesgue  
We show that the normalized volumes of these polytopes enumerate circular extensions of certain partial cyclic orders.  ...  We introduce several classes of polytopes contained in [0, 1] n and cut out by inequalities involving sums of consecutive coordinates.  ...  to the enumeration and refined enumeration of the circular extensions of the latter.  ... 
doi:10.5802/ahl.33 fatcat:rfbw52ctcnd2hegyelpbqusese

Extensions of partial cyclic orders and consecutive coordinate polytopes [article]

Arvind Ayyer and Matthieu Josuat-Vergès and Sanjay Ramassamy
2019 arXiv   pre-print
We show that the normalized volumes of these polytopes enumerate circular extensions of certain partial cyclic orders.  ...  We also provide a combinatorial interpretation of the Ehrhart h^*-polynomials of some of these polytopes in terms of descents of total cyclic orders.  ...  as the case k = 2 of the multidimensional boustrophedon.  ... 
arXiv:1803.10351v3 fatcat:lrcic7iczfaevlqwjvxu3lg2ve

Lattice Path Enumeration [article]

C. Krattenthaler
2017 arXiv   pre-print
This is a survey of results in the enumeration of lattice paths.  ...  LATTICE PATH ENUMERATION . LATTICE PATH ENUMERATION . LATTICE PATH ENUMERATION . LATTICE PATH ENUMERATION . LATTICE PATH ENUMERATION . LATTICE PATH ENUMERATION .  ...  Similarly, the result of Niederhausen on the enumeration of paths in the plane integer lattice subject to a piece-wise linear boundary, which was presented in Section 10.6, has a multidimensional extension  ... 
arXiv:1503.05930v3 fatcat:pf67gkqngng33ipma6uca6pd34

Parallel Shortest Lattice Vector Enumeration on Graphics Cards [chapter]

Jens Hermans, Michael Schneider, Johannes Buchmann, Frederik Vercauteren, Bart Preneel
2010 Lecture Notes in Computer Science  
Our implementation is almost 5 times faster in high lattice dimensions. Exhaustive search is one of the main building blocks for lattice basis reduction in cryptanalysis.  ...  In this paper we present an algorithm for parallel exhaustive search for short vectors in lattices. This algorithm can be applied to a wide range of parallel computing systems.  ...  We thankÖzgür Dagdelen for creating some of the initial ideas of parallelizing lattice enumeration and Benjamin Milde, Chen-Mou Cheng, and Bo-Yin Yang for the nice discussions and helpful ideas.  ... 
doi:10.1007/978-3-642-12678-9_4 fatcat:ewdokfhpmnakfk7rr5f2lchdxa

Lattice Path Enumeration [chapter]

Christian Krattenthaler
2015 Handbook of Enumerative Combinatorics  
Similarly, the result of Niederhausen on the enumeration of paths in the plane integer lattice subject to a piece-wise linear boundary, which was presented in Section 10.6, has a multidimensional extension  ...  in lattice path enumeration.  ... 
doi:10.1201/b18255-13 fatcat:hbkx2ouot5hfbevwkomrtltvbi

Page 2669 of Mathematical Reviews Vol. , Issue 82f [page]

1982 Mathematical Reviews  
Gyarmathi (Debrecen) 82f:68034 82f:68035 Ozgiiler, Biilent; Hiiseyin, Ozay 82f:68036 On the inversion of multidimensional polynomial matrices. IEEE Trans.  ...  P i, =0 i,=0 i,=0 This letter provides an algorithmic format which uses the main result of the authors’ article [op. cit.] for the inversion of the multidimensional polynomial matrix given in that article  ... 

Non-rational Narain CFTs from codes over F_4 [article]

Anatoly Dymarsky, Adar Sharon
2021 arXiv   pre-print
From the modular bootstrap point of view we formulate a polynomial ansatz for the partition function which reduces modular invariance to a handful of algebraic easy-to-solve constraints.  ...  We construct a map between a class of codes over F_4 and a family of non-rational Narain CFTs.  ...  Classification of Enumerator Polynomials We now attempt to classify the extended enumerator polynomials of the codes of N-type.  ... 
arXiv:2107.02816v1 fatcat:naa2nxtwinbujip2tvpmfg7ike

On Ehrhart polynomials and probability calculations in voting theory

Dominique Lepelley, Ahmed Louichi, Hatem Smaoui
2007 Social Choice and Welfare  
of linear constraints.  ...  In voting theory, analyzing the frequency of an event (e.g. a voting paradox), under some specific but widely used assumptions, is equivalent to computing the exact number of integer solutions in a system  ...  De Loera et al. (2004) developed the program LattE, a computer package for lattice point enumeration, which contains the first implementation of the technique of Barvinok for enumerating non-parametric  ... 
doi:10.1007/s00355-007-0236-1 fatcat:c6imqko3ijfibozl6rhgd46evy

Random Sampling Revisited: Lattice Enumeration with Discrete Pruning [chapter]

Yoshinori Aono, Phong Q. Nguyen
2017 Lecture Notes in Computer Science  
In 2003, Schnorr introduced Random sampling to find very short lattice vectors, as an alternative to enumeration.  ...  In this paper, we introduce lattice enumeration with discrete pruning, which generalizes random sampling and its variants, and provides a novel geometric description based on partitions of the n-dimensional  ...  = ∪ t∈U C(t) The algorithm performs exactly k partition-enumerations, where k = #U is the number of cells of discrete pruning, and each partition-enumeration runs in polynomial time by definition of the  ... 
doi:10.1007/978-3-319-56614-6_3 fatcat:dodceqqlbvddfo7jq7m6ckpnay

Polynomial indexing of integer lattice-points I. General concepts and quadratic polynomials

John S. Lew, Arnold L. Rosenberg
1978 Journal of Number Theory  
a copy of the Fueter-P6lya paper in Zurich, George Pblya for providing a confirmation of our bibliographical search, together with a reprint, and Donald J.  ...  Lewis for considering numerous aspects of this work during its revision.  ...  Moreover Chowla 161 exhibits an m-variable generalization of the polynomial (1.1) which effects a direct polynomial enumeration of the m-dimensional positive lattice.  ... 
doi:10.1016/0022-314x(78)90035-5 fatcat:v7cylztvizgihpvulzhfgym4xe
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