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III. Memoir on the theory of the partitions of numbers. —Part V. Partitions in two-dimensional space [PDF]
Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 1911 In previous papers I have broached the question of the two-dimensional partitions of numbers—or, say, the partitions in a plane—without, however, having succeeded in establishing certain conjectured formulas of enumeration. The parts of such partitions are placed at the nodes of a complete, or of an incomplete, lattice in two dimensions, in such wise ...
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Ehrhart Polynomials of a Cyclic Polytopes [PDF]
Engineering and Technology Journal, 2009 Computing the volume of a polytope in Rn is a very important subject indifferent areas of mathematic. A pplications range from the very pure (number theory, toric Hilbert functions, Kostant's partition function in representation theory) to the most ...
Shatha Assaad Salman, Fatema Ahmed Sadeq
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Annals of Mathematics and PhysicsThis paper introduces a novel approach to estimating the sum of prime numbers by leveraging insights from partition theory, prime number gaps, and the angles of triangles.
Zaman Budee U
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Entanglement distillation protocols and number theory (17 pages) [PDF]
, 2005 We show that the analysis of entanglement distillation protocols for qudits of arbitrary dimension D benefits from applying basic concepts from number theory, since the set Z{sub D}{sup n} associated with Bell diagonal states is a module rather than a ...
H. Bombin, M. Martin-Delgado
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The Rank and Minimal Border Strip Decompositions of a Skew Partition [PDF]
, 2001 Nazarov and Tarasov recently generalized the notion of the rank of a partition to skew partitions. We give several characterizations of the rank of a skew partition and one possible characterization that remains open.
Stanley, Richard P.
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Fundamental vortices, wall-crossing, and particle-vortex duality
Journal of High Energy Physics, 2017 We explore 1d vortex dynamics of 3d supersymmetric Yang-Mills theories, as inferred from factorization of exact partition functions. Under Seiberg-like dualities, the 3d partition function must remain invariant, yet it is not a priori clear what should ...
Chiung Hwang, Piljin Yi, Yutaka Yoshida
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3d N $$ \mathcal{N} $$ = 3 generalized Giveon-Kutasov duality
Journal of High Energy Physics, 2022 We generalize the Giveon-Kutasov duality for the 3d N $$ \mathcal{N} $$ = 3 U(N) k,k+nN Chern-Simons matter gauge theory with F fundamental hypermultiplets by introducing SU(N) and U(1) Chern-Simons levels differently.
Naotaka Kubo, Keita Nii
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Srinivasa Ramanujan (1887‐1920) and the theory of partitions of numbers and statistical mechanics a centennial tribute [PDF]
International Journal of Mathematics and Mathematical Sciences, 1987 This centennial tribute commemorates Ramanujan the Mathematician and Ramanujan the Man. A brief account of his life, career, and remarkable mathematical contributions is given to describe the gifted talent of Srinivasa Ramanujan. As an example of his creativity in mathematics, some of his work on the theory of partition of numbers has been presented ...
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On the Isometric Path Partition Problem [PDF]
Discussiones Mathematicae Graph Theory, 2018 The isometric path cover (partition) problem of a graph consists of finding a minimum set of isometric paths which cover (partition) the vertex set of the graph.
P. Manuel
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Odd values of the Klein j-function and the cubic partition function [PDF]
, 2015 In this note, using entirely algebraic or elementary methods, we determine a new asymptotic lower bound for the number of odd values of one of the most important modular functions in number theory, the Klein $j$-function.
Zanello, Fabrizio
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