Results 1 to 10 of about 258,418 (162)
S-Restricted Compositions Revisited [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years.
Behrouz Zolfaghari +2 more
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Integer composition, connection Appell constants and Bell polynomials
Journal of Numerical Analysis and Approximation Theory, 2021 We introduce an explicit form of the connection coefficients for Appell polynomial sequences via Toeplitz-Hessenberg matrix determinants. Generalizing, we give an explicit form of the connection coefficients for arbitrary polynomial sequences and ...
Nataliia Luno
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ON MULTIPLICATIVE COMPOSITIONS OF INTEGERS [PDF]
Mathematika, 2017 We consider an arithmetic function defined independently by John G. Thompson andGreg Simay, with particular attention to its mean value, and its maximal size, and the analyticnature of its Dirichlet series generating function.
Montgomery, Hugh, Tenenbaum, Gerald
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Integer factoring and compositeness witnesses [PDF]
Journal of Mathematical Cryptology, 2020 AbstractWe describe a reduction of the problem of factorization of integers n ≤ x in polynomial-time (log x)M+O(1) to computing Euler’s totient function, with exceptions of at most xO(1/M) composite integers that cannot be factored at all, and at most x exp $\begin{array}{} \displaystyle \left(-\frac{c_M(\log\log x)^3}{(\log\log\log x)^2}\right) \end ...
Pomykała Jacek, Radziejewski Maciej
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The first ascent of size $d$ or more in compositions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 A composition of a positive integer $n$ is a finite sequence of positive integers $a_1, a_2, \ldots, a_k$ such that $a_1+a_2+ \cdots +a_k=n$. Let $d$ be a fixed nonnegative integer.
Charlotte Brennan, Arnold Knopfmacher
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Part-products of S-restricted integer compositions [PDF]
Applicable Analysis and Discrete Mathematics, 2013 If S is a cofinite set of positive integers, an "S-restricted composition of n" is a sequence of elements of S, denoted ?? = (?1, ?2, ... ), whose sum is n. For uniform random S-restricted compositions, the random variable B(??) = ?i ?i is asymptotically lognormal. (A precise statement of the theorem includes an error term to bound the rate
Schmutz, Eric, Shapcott, Caroline
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The topology of restricted partition posets [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 For each composition $\vec{c}$ we show that the order complex of the poset of pointed set partitions $Π ^• _{\vec{c}}$ is a wedge of $β\vec{c}$ spheres of the same dimensions, where $β\vec{c}$ is the number of permutations with descent composition ^$\vec{
Richard Ehrenborg, JiYoon Jung
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A Littlewood-Richardson type rule for row-strict quasisymmetric Schur functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We establish several properties of an algorithm defined by Mason and Remmel (2010) which inserts a positive integer into a row-strict composition tableau.
Jeffrey Ferreira
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Record statistics in integer compositions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 A $\textit{composition}$ $\sigma =a_1 a_2 \ldots a_m$ of $n$ is an ordered collection of positive integers whose sum is $n$. An element $a_i$ in $\sigma$ is a strong (weak) $\textit{record}$ if $a_i> a_j (a_i \geq a_j)$ for all $j=1,2,\ldots,i-1$. Furthermore, the position of this record is $i$. We derive generating functions for the total number of
Knopfmacher, Arnold, Mansour, Toufik
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Query-Efficient Locally Decodable Codes of Subexponential Length [PDF]
, 2010 We develop the algebraic theory behind the constructions of Yekhanin (2008) and Efremenko (2009), in an attempt to understand the ``algebraic niceness'' phenomenon in $\mathbb{Z}_m$.
Chee, Yeow Meng +4 more
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