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Binary Prime Tableau Sequences
[article]
2017
arXiv
pre-print
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This paper proposes a new class of random sequences called binary primes tableau (PT) sequences that have potential applications in cryptography and communications. ...
The PT sequence of rank p is obtained from numbers arranged in a tableau with p columns where primes are marked off until each column has at least one prime and where the column entries are added modulo ...
The CBPT P for p is constructed as Definition 3.2 Binary Primes Tableau Sequence (BPT): The sequence obtained by adding CBPT P entries column-wise mod 2, will be called a Binary Primes Tableau sequence ...
arXiv:1704.08718v1
fatcat:uhtxmbe5dbfeffg4ioxwwe2o2a
Around Pelikán's conjecture on very odd sequences
2005
Manuscripta mathematica
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2005 accepted arXiv:math/0407084v2 fatcat:zatifzfrevegrjlxiiiktbgsbmOther Versions
the number of very odd sequences of length n. ...
Very odd sequences were introduced in 1973 by J. Pelikan who conjectured that there were none of length >=5. ...
Lemma 1 We have S(n) > 0 iff there exists a [2n, n] extended binary cyclic code. ...
doi:10.1007/s00229-005-0554-5
fatcat:yag5zecvbjc5rfp3wfu3ppeqiu
Dismal Arithmetic
[article]
2011
arXiv
pre-print
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This paper studies basic number theory in this world, including analogues of the primes, number of divisors, sum of divisors, and the partition function. ...
the tableau for p 2 q, that is still true for p 2 q ′ ). ...
templates, (b) all templates, (c) base 10 primes obtained by promoting the binary templates, and (d) base 10 primes obtained by promoting all the templates. k (a) (b) (c) (d) We can reduce the list of ...
arXiv:1107.1130v2
fatcat:363uzmvl5bcwthktjwdokbv4ym
Congruences in character tables of symmetric groups
[article]
2020
arXiv
pre-print
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The word of a non-empty partition λ is the unique binary sequence of shape λ that starts with 0 and ends with 1; the word of the empty partition is the empty sequence. ...
Cascades By the word of a partition λ we mean the binary sequence w(λ) obtained from λ by writing 0 under each column, 1 alongside each row, and reading clockwise, e.g. the word of (4, 2) is 001001: 1 ...
arXiv:1908.03741v2
fatcat:focodssp2vex5kjm7uff6lprxi
Decidability results in automata and process theory
[chapter]
1996
Lecture Notes in Computer Science
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However, the intention of a process is to allow an analysis of its runtime behaviour rather than simply the sequences of transitions which lead to a final state. ...
The norm of a process state a E S, written norm(a), is the length of the shortest transition sequence from that state to a terminal state, that is, a state from which no transitions evolve. ...
But then this sequence provides a tableau with an infinite path through it, which by the first part cannot be. [] We now proceed to show the soundness and completeness of the tableau system. ...
doi:10.1007/3-540-60915-6_4
fatcat:zoxvo4dlergqdfkugtlypihd5i
Tropical Geometry, Quantum Affine Algebras, and Scattering Amplitudes
[article]
2024
arXiv
pre-print
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2023 pre-print arXiv:2303.05618v1 fatcat:qk2mkwbmqjdtbe5amhvf2l4iuaOther Versions
The connection allows us to study important and difficult questions in these areas: (1) We give a systematic construction of prime modules (including prime non-real modules) of quantum affine algebras ...
We give a general formula of u-variables using prime tableaux (corresponding to prime modules of quantum affine algebras of type A) and Auslander-Reiten quivers of Grassmannian cluster categories. (3) ...
k, [n]) (in finite type, all prime tableau are real). ...
arXiv:2303.05618v4
fatcat:jjx24vwuxnhnvlejgqjc2uoxjm
Permuted composition tableaux, 0-Hecke algebra and labeled binary trees
[article]
2018
arXiv
pre-print
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We provide a bijection between two-columned tableaux and labeled binary trees. ...
permuted composition tableaux is to enumerate all possible ordered pairs of permutations (σ_1,σ_2) that can be obtained by standardizing the entries in two adjacent columns of an arbitrary composition tableau ...
Note that the run sequence determines the maximal labeled left path decomposition of the resulting binary tree. ...
arXiv:1712.05008v2
fatcat:g2kx534unzbgli5fazfz6aqpsq
Genomic tableaux
2016
Journal of Algebraic Combinatorics
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2016 pre-print arXiv:1603.08490v1 fatcat:5auab43wqzczzatjgjmqkm772m
Convert partitions inside a k × (n − k) rectangle to binary sequences in the following way. ...
Starting at the upper right corner of the k × (n − k) rectangle, construct a lattice path from the binary sequence by reading each segment (−1, 0) as 0 and each segment (0, −1) as 1. ...
doi:10.1007/s10801-016-0720-8
fatcat:7v5uok2zebfbnobfqhe3dv7vyu
Toric Ideals of Phylogenetic Invariants
2005
Journal of Computational Biology
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For the Jukes-Cantor and Kimura models on a binary tree, our Gröbner basis consists of quadrics, cubics and quartics. ...
Several widely used models for biological sequences have transition matrices that can be diagonalized by means of the Fourier transform of an abelian group. ...
The class of group-based models includes the Jukes-Cantor model, for either binary or DNA sequences, and the Kimura models, with two or three parameters. ...
doi:10.1089/cmb.2005.12.204
pmid:15767777
fatcat:sq2ar7u4ufhjdmji5z2jts3pmq
Modular irreducible representations of the symmetric group as linear codes
2004
European journal of combinatorics (Print)
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The first embedding is into the permutation representation induced from the column group of a standard Young tableau of shape λ. ...
Assume a prime number p and a p-regular partition λ of n. ...
The sequence of coefficients of the monomials x i x k (numbered lexicographically) is 1, 1, 2, 2, 1, 2, 2, 2, 2, 0. ...
doi:10.1016/j.ejc.2003.10.009
fatcat:jv5zuijufnablpcdmmwsa2xc2e
The semantics of BI and resource tableaux
2005
Mathematical Structures in Computer Science
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If , then there is a closed tableau sequence for . Proof. Suppose there is no closed tableau sequence for . ...
A bunch is said to be prime if it verifies that implies or . A prime extension of a bunch is a bunch such that is prime and . ...
If there is no closed tableau for . Thus, the tableau construction procedure yields a tableau with a completed branch . ...
doi:10.1017/s0960129505004858
fatcat:n2gktzqns5d57pq3phcf6mlvcm
A Generalized RSK for Enumerating Linear Series on n-pointed Curves
2023
Algebraic Combinatorics
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Define an L-tableau with parameters (g, r, d) to be a way of filling the boxes of an (r + 1) × (d − r) grid with rg "red" integers and (d − r)(r + 1) − rg "blue" integers such that: ...
We give a bijection, generalizing the well-known RSK correspondence, between the tableaux in question and the (r +1)-ary sequences of length g, and we explore our bijection's combinatorial properties. ...
Consider the L-tableau with parameters (5, 1, 6) below: 3 0 1 1 1 1 2 4 5 0 The bijection φ applied to the red tableau above gives: which corresponds under RSK to the binary sequence 0, 1, 0, 0, 1. 3.4 ...
doi:10.5802/alco.250
fatcat:lpga3rk45faw5dfrahs6xs6pce
A linearized stabilizer formalism for systems of finite dimension
[article]
2012
arXiv
pre-print
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Proper stabilizer tableaus for d prime and d odd For d either prime or odd, we wish to show that any sequence S 1 , . . . , S ℓ ∈ P ⊗n d of commuting Pauli operators (each with order at most d) may be ...
Thus, all stabilizer tableaus are proper for d odd. It remains to prove the result for the binary case d = 2. ...
As we have remarked previously, the familiar case for d prime corresponds to η = 1 provided that P does not commute with all elements of G S . ...
arXiv:1102.3354v4
fatcat:6ky7jvbv2raexoloob2zrbytxe
SequenceL
2010
Proceedings of the 5th ACM SIGPLAN workshop on Declarative aspects of multicore programming - DAMP '10
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of tableaus generated when a binary tree of integers is multiplied by a scalar: [1,2,3],[4,5,6],[7,8,9]]*[10,20,30]
[[1,2,3]*[10,20,30],[4,5,6]*[10,20,30],
[7,8,9]*[10,20,30]]
[[1*10,2*20,3*30], ...
Given a tableau: [1,2,3] * 5 The consume will remove the expression from the tableau. ...
doi:10.1145/1708046.1708057
dblp:conf/popl/NemanichCR10
fatcat:bf5hhyuah5acjny6mbemzov4ce
Chains of binary paths and shifted tableaux
[article]
2019
arXiv
pre-print
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In this paper, a natural bijection between multichains of binary paths and shifted tableaux is presented, and it is used for the enumeration of the chains with maximum length from a given path P to the ...
A Dyck path with only one return point is called prime. ...
This ordering is better understood by considering the following alternative encoding of binary paths: Every P ∈ P n can be described uniquely by the sequence (h i (P )) i∈ [n] of the heights of its points ...
arXiv:1911.13013v1
fatcat:yqhayuvikbctxapey2nqvmpu7i
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