Parity results for broken 11-diamond partitions

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. In particular, we generalize the congruences due to Dai by utilizing an iden...

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Veröffentlicht in:Open mathematics (Warsaw, Poland) Poland), 2019-05, Vol.17 (1), p.402-406
1. Verfasser: Wu, Yunjian
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Sprache:eng
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Zusammenfassung: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. In particular, we generalize the congruences due to Dai by utilizing an identity due to Newman. Furthermore, we prove some strange congruences modulo 2 for broken 11-diamond partition functions. For example, we prove that if is a prime with ≠ 23 and (2 + 1) ≡ 1 (mod 2), then for any ≥ 0, (2 + 1) ≡ 1 (mod 2), where ) is the number of broken 11-diamond partitions of
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2019-0031