Results 11 to 20 of about 1,248 (76)
Representations by degenerate Daehee polynomials
Open Mathematics, 2022 In this paper, we consider the problem of representing any polynomial in terms of the degenerate Daehee polynomials and more generally of the higher-order degenerate Daehee polynomials.
Kim Taekyun +3 more
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Flip-sort and combinatorial aspects of pop-stack sorting [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Flip-sort is a natural sorting procedure which raises fascinating combinatorial questions. It finds its roots in the seminal work of Knuth on stack-based sorting algorithms and leads to many links with permutation patterns. We present several structural,
Andrei Asinowski +2 more
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On 2-adic orders of some binomial sums [PDF]
, 2010 We prove that for any nonnegative integers $n$ and $r$ the binomial sum $$ \sum_{k=-n}^n\binom{2n}{n-k}k^{2r} $$ is divisible by $2^{2n-\min\{\alpha(n),\alpha(r)\}}$, where $\alpha(n)$ denotes the number of 1's in the binary expansion of $n$.
Pan, Hao, Sun, Zhi-Wei
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Compositions of positive integers with 2s and 3s
Demonstratio Mathematica, 2023 In this article, we consider compositions of positive integers with 2s and 3s. We see that these compositions lead us to results that involve Padovan numbers, and we give some tiling models of these compositions.
Dişkaya Orhan, Menken Hamza
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MacMahon’s statistics on higher-dimensional partitions
Forum of Mathematics, Sigma, 2023 We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between d-dimensional partitions and d-dimensional arrays of nonnegative integers.
Alimzhan Amanov, Damir Yeliussizov
doaj +1 more source
1974 conjecture of Andrews on partitions
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 21, Page 1097-1104, 2004., 2004 The case k = a of the 1974 conjecture of Andrews on two partition functions Aλ,k,a(n) and Bλ,k,a(n) was proved by the first author and Sudha (1993) and the case k = a + 1 was established by the authors (2000). In this paper, we prove that the conjecture is false and give a revised conjecture for a particular case when λ is even.
Padmavathamma, M. R. Salestina
wiley +1 more source
Catalan Traffic and Integrals on the Grassmannians of Lines [PDF]
, 2007 We prove that certain numbers occurring in a problem of paths enumeration, studied by Niederhausen (Catlan Traffic at the Beach, The Electronic Journal of Combinatorics, 9, (2002), 1--17), are top intersection numbers in the cohomology ring of the ...
Fulton +6 more
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A quantum field theoretical representation of Euler‐Zagier sums
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 3, Page 127-148, 2002., 2002 We establish a novel representation of arbitrary Euler‐Zagier sums in terms of weighted vacuum graphs. This representation uses a toy quantum field theory with infinitely many propagators and interaction vertices. The propagators involve Bernoulli polynomials and Clausen functions to arbitrary orders.
Uwe Müller, Christian Schubert
wiley +1 more source
Evaluation of integrals with hypergeometric and logarithmic functions
Open Mathematics, 2018 We provide an explicit analytical representation for a number of logarithmic integrals in terms of the Lerch transcendent function and other special functions.
Sofo Anthony
doaj +1 more source
A new proof of some identities of Bressoud
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 10, Page 627-633, 2002., 2002 We provide a new proof of the following two identities due to Bressoud: ∑m=0Nqm2[Nm]=∑m=−∞∞(−1)mqm(51m+)/2 [ 2NN+2m], ∑m=0Nqm2+m[Nm]=(1/(1−qN+1))∑m=−∞∞(−1)m×qm(53m+)/2 [ 22N+N+22m+], which can be considered as finite versions of the Rogers‐Ramanujan identities.
Robin Chapman
wiley +1 more source