Results 21 to 30 of about 171,184 (277)
Congruences for the Apéry numbers modulo p³ [PDF]
Notes on Number Theory and Discrete MathematicsLet {Aₙ'} be the Apéry numbers given by Aₙ'=\Σⁿₖ₌ₒ$binom{n}{k}$²$binom{n+k}{k}$. For any prime p≡3 (mod 4) we show that A'_{(p-1)/2}≡p²/3$binom{(p-3)/2}{(p-3)/4}$² (mod p³). Let {tₙ} be given by t₀=1, t₁=5 and tₙ₊₁=(8n²+12n+5)tₙ-4n²(2n+1)²tₙ₋₁ (n≥1).
Zhi-Hong Sun
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Generalized Tepper’s Identity and Its Application
Mathematics, 2020 The aim of this paper is to study the Tepper identity, which is very important in number theory and combinatorial analysis. Using generating functions and compositions of generating functions, we derive many identities and relations associated with the ...
Dmitry Kruchinin +2 more
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Dendriform structures for restriction-deletion and restriction-contraction matroid Hopf algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 We endow the set of isomorphism classes of matroids with a new Hopf algebra structure, in which the coproduct is implemented via the combinatorial operations of restriction and deletion.
Nguyen Hoang-Nghia +2 more
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Specification of neuronal identities by feedforward combinatorial coding.
PLoS Biology, 2007 Neuronal specification is often seen as a multistep process: earlier regulators confer broad neuronal identity and are followed by combinatorial codes specifying neuronal properties unique to specific subtypes.
Magnus Baumgardt +4 more
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A Note on the Difference of Powers and Falling Powers
International Journal of Mathematics and Mathematical Sciences, 2021 Combinatorial sums and binomial identities have appeared in many branches of mathematics, physics, and engineering. They can be established by many techniques, from generating functions to special series.
Taoufik Sabar
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A two-sided Faulhaber-like formula involving Bernoulli polynomials
Comptes Rendus. Mathématique, 2020 We give a new identity involving Bernoulli polynomials and combinatorial numbers. This provides, in particular, a Faulhaber-like formula for sums of the form $1^m(n-1)^m+2^m(n-2)^m+\dots +(n-1)^m1^m$ for positive integers $m$ and $n$.
Barbero G., J. Fernando +2 more
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Convolution Powers of the Identity [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We study convolution powers $\mathtt{id}^{\ast n}$ of the identity of graded connected Hopf algebras $H$. (The antipode corresponds to $n=-1$.) The chief result is a complete description of the characteristic polynomial - both eigenvalues and ...
Marcelo Aguiar, Aaron Lauve
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On Combinatorial Identities of Engbers and Stocker
Integers, 2017 See the abstract in the attached pdf.
Horst Alzer, Helmut Prodinger
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Descents of $\lambda$-unimodal cyclic permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We prove an identity conjectured by Adin and Roichman involving the descent set of $\lambda$-unimodal cyclic permutations. These permutations appear in the character formulas for certain representations of the symmetric group and these formulas are ...
Kassie Archer
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Quantitative Plant Biology, 2023 The 1991 review paper by Coen and Meyerowitz on the control of floral organ development set out the evidence available at that time, which led to the now famous ABC model of floral organ identity control.
Kay Schneitz
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