Results 21 to 30 of about 505,916 (139)
Arc Spaces and Rogers-Ramanujan Identities [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Arc spaces have been introduced in algebraic geometry as a tool to study singularities but they show strong connections with combinatorics as well. Exploiting these relations we obtain a new approach to the classical Rogers-Ramanujan Identities.
Clemens Bruschek +2 more
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The Reading Teacher, Volume 77, Issue 2, Page 189-198, September/October 2023., 2023 Abstract This article explores the potential of using children's literature in elementary mathematics classrooms as contexts for students to understand more fully the issues of equity, diversity, and inclusion. Informed by culturally responsive pedagogy, opportunities to link children's literature to mathematics education create cultural relevance for ...
Evan Throop Robinson
wiley +1 more source
Further Rogers-Ramanujan type identities for modified lattice paths [PDF]
, 2023 Recently, the authors introduced the modified lattice paths which generalize Agarwal-Bressoud weighted lattice paths. Using these new objects they interpreted combinatorially two basic series identities which led to two new combinatorial Rogers-Ramanujan
Ashok Kumar Agarwal, Sachdeva, Rachna
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Orthogonality Property of the Discrete q‐Hermite Matrix Polynomials
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 In this paper, we prove that the solution of the autonomous q‐difference system DqY(x) = AY(qx) with the initial condition Y(0) = Y0 where A is a constant square complex matrix, Dq is the Jackson q‐derivative and 0 < q < 1, is asymptotically stable if and only if ℜ(λ) < 0 for all λ ∈ σ(A) where σ(A) is the set of all eigenvalues of A (the spectrum of A)
Ahmed Salem +3 more
wiley +1 more source
POLYNOMIAL IDENTITIES OF THE ROGERS-RAMANUJAN TYPE [PDF]
International Journal of Modern Physics A, 1995 Presented are polynomial identities which imply generalizations of Euler and Rogers-Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by establishing a graphical one-to-one correspondence between those two kinds of restricted partitions.
Foda, Omar, Quano, Yas-Hiro
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The Rogers-Ramanujan Identities [PDF]
Turkish Journal of Analysis and Number Theory, 2016 In 1894, Rogers found the two identities for the first time. In 1913, Ramanujan found the two identities later and then the two identities are known as The Rogers-Ramanujan Identities. In 1982, Baxter used the two identities in solving the Hard Hexagon Model in Statistical Mechanics.
Fazlee Hossain +2 more
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An extension to overpartitions of Rogers-Ramanujan identities for even moduli [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 We investigate class of well-poised basic hypergeometric series $\tilde{J}_{k,i}(a;x;q)$, interpreting these series as generating functions for overpartitions defined by multiplicity conditions.
Sylvie Corteel +2 more
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Axioms, 2013 Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functions J(q) and K(q) of order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan
Nasser Abdo Saeed Bulkhali +1 more
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Sums of Series of Rogers Dilogarithm Functions [PDF]
, 2007 Some sums of series of Rogers dilogarithm functions are established by Abel’s functional ...
Qi, Feng, Hoorfar, Abdolhossein
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Colored Partitions and the Fibonacci Sequence
Trends in Computational and Applied Mathematics, 2006 We present interesting combinatorial interpretations for the Fibonacci numbers in terms of colored partitions obtained by using finite versions of two identities of the Rogers-Ramanujan type. New formula for the Fibonacci numbers is also given.
J.P.O. Santos, M. Ivkovic
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