Results 1 to 10 of about 829 (63)
Correlations in totally symmetric self‐complementary plane partitions
Transactions of the London Mathematical Society, 2021 Totally symmetric self‐complementary plane partitions (TSSCPPs) are boxed plane partitions with the maximum possible symmetry. We use the well‐known representation of TSSCPPs as a dimer model on a honeycomb graph enclosed in 1/12 of a hexagon with free ...
Arvind Ayyer, Sunil Chhita
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On Graham partitions twisted by the Legendre symbol
Open Mathematics, 2023 We investigate when there is a partition of a positive integer nn, n=f(λ1)+f(λ2)+⋯+f(λℓ),n=f\left({\lambda }_{1})+f\left({\lambda }_{2})+\cdots +f\left({\lambda }_{\ell }), satisfying that 1=χp(λ1)λ1+χp(λ2)λ2+⋯+χp(λℓ)λℓ,1=\frac{{\chi }_{p}\left({\lambda }
Kim Byungchan +5 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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Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture
Forum of Mathematics, Sigma, 2020 One of the oldest outstanding problems in dynamical algebraic combinatorics is the following conjecture of P. Cameron and D. Fon-Der-Flaass (1995): consider a plane partition P in an $a \times b \times c$ box ${\sf B}$ . Let $\Psi (P)$
Rebecca Patrias, Oliver Pechenik
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An Extreme Family of Generalized Frobenius Numbers [PDF]
, 2011 We study a generalization of the \emph{Frobenius problem}: given $k$ positive relatively prime integers, what is the largest integer $g_0$ that cannot be represented as a nonnegative integral linear combination of these parameters?
Beck, Matthias, Kifer, Curtis
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Compositions inside a rectangle and unimodality [PDF]
, 2007 Let c^{k,l}(n) be the number of compositions (ordered partitions) of the integer n whose Ferrers diagram fits inside a k-by-l rectangle. The purpose of this note is to give a simple, algebraic proof of a conjecture of Vatter that the sequence c^{k,l}(0),
Sagan, Bruce E.
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Parity results for broken 11-diamond partitions
Open Mathematics, 2019 Recently, Dai proved new infinite families of congruences modulo 2 for broken 11-diamond partition functions by using Hecke operators. In this note, we establish new parity results for broken 11-diamond partition functions.
Wu Yunjian
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Some congruences for 3-component multipartitions
Open Mathematics, 2016 Let p3(n) denote the number of 3-component multipartitions of n. Recently, using a 3-dissection formula for the generating function of p3(n), Baruah and Ojah proved that for n ≥ 0, p3(9n + 5) ≡ 0 (mod 33) and p3 (9n + 8) ≡ 0 (mod 34).
Zhao Tao Yan, Jin Lily J., Gu C.
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Power partitions and saddle-point method [PDF]
, 2019 For $k\geqslant 1$, denote by $p_k(n)$ the number of partitions of an integer $n$ into $k$-th powers. In this note, we apply the saddle-point method to provide a new proof for the well-known asymptotic expansion of $p_k(n)$.
Li, Yali, Tenenbaum, Gérald, Wu, Jie
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On Partitions and Arf Semigroups
Open Mathematics, 2019 In this study we examine some combinatorial properties of the Arf semigroup. In previous work, the author and Karakaş, Gümüşbaş defined an Arf partition of a positive integer n. Here, we continue this work and give new results on Arf partitions.
Tutaş Nesrin
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