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pro vyhledávání: '"Hopkins, Brian"'
Recently, Blecher and Knopfmacher applied the notion of fixed points to integer partitions. This has already been generalized and refined in various ways such as $h$-fixed points for an integer parameter $h$ by Hopkins and Sellers. Here, we consider
Externí odkaz:
http://arxiv.org/abs/2401.06254
Autor:
Hopkins, Brian
Publikováno v:
Enumer. Combin. Appl. 4:4 (2024) S2R26
Recently, Blecher and Knopfmacher explored the notion of fixed points in integer partitions. Here, we distinguish partitions with a fixed point by which value is fixed and analyze the resulting triangle of integers. In particular, we confirm various
Externí odkaz:
http://arxiv.org/abs/2311.11433
Autor:
Hopkins, Brian, Tangboonduangjit, Aram
In 2013, Joerg Arndt recorded that the Fibonacci numbers count integer compositions where the first part is greater than the second, the third part is greater than the fourth, etc. We provide a new combinatorial proof that verifies his observation us
Externí odkaz:
http://arxiv.org/abs/2307.12434
Autor:
Hopkins, Brian, Sellers, James A.
Publikováno v:
Discrete Math. 347 (2024) 113938
Recently, Blecher and Knopfmacher explored the notion of fixed points in integer partitions and hypothesized on the relative number of partitions with and without a fixed point. We resolve their open question by working fixed points into a growing nu
Externí odkaz:
http://arxiv.org/abs/2305.05096
Autor:
Hopkins, Brian, McClintock, Peter
Publikováno v:
History Ireland, 2023 Jul 01. 31(4), 40-43.
Externí odkaz:
https://www.jstor.org/stable/27233768
Publikováno v:
Electron. J. Combin. 29 (2022) P2.11
Several authors have recently considered the smallest positive part missing from an integer partition, known as the minimum excludant or mex. In this work, we revisit and extend connections between Dyson's crank statistics, the mex, and Frobenius sym
Externí odkaz:
http://arxiv.org/abs/2108.09414
Autor:
Hopkins, Brian, Sellers, James A.
Publikováno v:
In Discrete Mathematics May 2024 347(5)
Publikováno v:
J. Combin. Theory Ser. A 185 (2022) 105523
Andrews and Newman have recently introduced the notion of the mex of a partition, the smallest positive integer that is not a part. The concept has been used since at least 2011, though, with connections to Frobenius symbols. Recently the parity of t
Externí odkaz:
http://arxiv.org/abs/2009.10873
Autor:
Hopkins, Brian, Ouvry, Stéphane
Publikováno v:
Combinatorial and Additive Number Theory IV, ed. Nathanson, Springer Proceedings 347 (2021) 307-321
Integer compositions with certain colored parts were introduced by Andrews in 2007 to address a number-theoretic problem. Integer compositions allowing zero as some parts were introduced by Ouvry and Polychronakos in 2019. We give a bijection between
Externí odkaz:
http://arxiv.org/abs/2008.04937
Autor:
Hopkins, Brian, Wang, Hua
Publikováno v:
J. Combin. 12(2) (2021) 355-377
Agarwal introduced $n$-color compositions in 2000 and most subsequent research has focused on restricting which parts are allowed. Here we focus instead on restricting allowed colors. After three general results, giving recurrence formulas for the ca
Externí odkaz:
http://arxiv.org/abs/2003.05291