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Solutions of modular bootstrap constraints from quantum codes
[article]
2020
arXiv
pre-print
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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
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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
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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
2019
Chinese Physics B
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2019 pre-print arXiv:1903.11959v1 fatcat:j2mi7s5tgjhvhe3aj3gymez2va
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
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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
2020
Annales Henri Lebesgue
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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]
2019
arXiv
pre-print
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2018 pre-print arXiv:1803.10351v2 fatcat:3lkfogw3qjf2poyhpqothdkokeOther Versions
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]
2017
arXiv
pre-print
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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]
2010
Lecture Notes in Computer Science
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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]
2015
Handbook of Enumerative Combinatorics
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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
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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]
2021
arXiv
pre-print
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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
2007
Social Choice and Welfare
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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]
2017
Lecture Notes in Computer Science
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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
1978
Journal of Number Theory
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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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