Results 11 to 20 of about 69 (69)
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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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
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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
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
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The log-concavity of the q-derangement numbers of type B
Open Mathematics, 2018 Recently, Chen and Xia proved that for n ≥ 6, the q-derangement numbers Dn(q) are log-concave except for the last term when n is even. In this paper, employing a recurrence relation for DnB(q) $\begin{array}{} \displaystyle D^B_n(q) \end{array ...
Liu Eric H., Du Wenjing
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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
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
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Some combinatorial matrices and their LU-decomposition
Special Matrices, 2020 Three combinatorial matrices were considered and their LU-decompositions were found. This is typically done by (creative) guessing, and the proofs are more or less routine calculations.
Prodinger Helmut
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Symmetry of Narayana Numbers and Rowvacuation of Root Posets
Forum of Mathematics, Sigma, 2021 For a Weyl group W of rank r, the W-Catalan number is the number of antichains of the poset of positive roots, and the W-Narayana numbers refine the W-Catalan number by keeping track of the cardinalities of these antichains.
Colin Defant, Sam Hopkins
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A new triple sum combinatorial identity
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 12, Page 761-763, 2002., 2002 We prove a new triple sum combinatorial identity derived from rp(x, y, z) = (x+y−z)p − (xp + yp − zp), extending a previous result by Sinyor et al.
Joseph Sinyor, Akalu Tefera
wiley +1 more source