Results 1 to 10 of about 74 (71)
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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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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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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A PROOF OF ANDREWS’ CONJECTURE ON PARTITIONS WITH NO SHORT SEQUENCES
Forum of Mathematics, Sigma, 2019 Our main result establishes Andrews’ conjecture for the asymptotic of the generating function for the number of integer partitions of $n$ without $k$ consecutive parts.
DANIEL M. KANE, ROBERT C. RHOADES
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Arithmetic properties for Andrews’ (48,6)- and (48,18)-singular overpartitions
Open Mathematics, 2019 Singular overpartition functions were defined by Andrews. Let Ck,i(n) denote the number of (k, i)-singular overpartitions of n, which counts the number of overpartitions of n in which no part is divisible by k and only parts ±i (mod k) may be overlined ...
Liu Eric H., Du Wenjing
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A Note on Graph Burning of Path Forests [PDF]
Discrete Mathematics & Theoretical Computer ScienceGraph burning is a natural discrete graph algorithm inspired by the spread of social contagion. Despite its simplicity, some open problems remain steadfastly unsolved, notably the burning number conjecture, which says that every connected graph of order $
Ta Sheng Tan, Wen Chean Teh
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