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pro vyhledávání: '"Allen, Michael P."'
In the first paper of this sequence, we provided an explicit hypergeometric modularity method by combining different techniques from the classical, $p$-adic, and finite field settings. In this article, we explore an application of this method from a
Externí odkaz:
http://arxiv.org/abs/2411.15116
We study the holomorphic projection of mixed mock modular forms involving sesquiharmonic Maass forms. As a special case, we numerically express the holomorphic projection of a function involving real quadratic class numbers multiplied by a certain th
Externí odkaz:
http://arxiv.org/abs/2411.05972
Autor:
Allen, Michael A.
Let $S_n$ and $S_{n,k}$ be, respectively, the number of subsets and $k$-subsets of $\mathbb{N}_n=\{1,\ldots,n\}$ such that no two subset elements differ by an element of the set $\mathcal{Q}$. We prove a bijection between such $k$-subsets when $\math
Externí odkaz:
http://arxiv.org/abs/2409.00624
Autor:
Allen, Michael A.
We consider the restricted subsets of $\mathbb{N}_n=\{1,2,\ldots,n\}$ with $q\geq1$ being the largest member of the set $\mathcal{Q}$ of disallowed differences between subset elements. We obtain new results on various classes of problem involving suc
Externí odkaz:
http://arxiv.org/abs/2210.08167
Autor:
Allen, Michael A.
Publikováno v:
Journal of Integer Sequences 25(9) Article 22.9.8 (2022)
We consider a two-parameter family of triangles whose $(n,k)$-th entry (counting the initial entry as the $(0,0)$-th entry) is the number of tilings of $N$-boards (which are linear arrays of $N$ unit square cells for any nonnegative integer $N$) with
Externí odkaz:
http://arxiv.org/abs/2209.01377
Autor:
Allen, Michael
In 2003, Rodriguez Villegas conjectured 14 supercongruences between hypergeometric functions arising as periods of certain families of rigid Calabi-Yau threefolds and the Fourier coefficients of weight 4 modular forms. Uniform proofs of these superco
Externí odkaz:
http://arxiv.org/abs/2202.05408
Autor:
Allen, Michael A., Edwards, Kenneth
Publikováno v:
Journal of Integer Sequences 25(7) Article 22.7.1 (2022)
We consider two families of Pascal-like triangles that have all ones on the left side and ones separated by $m-1$ zeros on the right side. The $m=1$ cases are Pascal's triangle and the two families also coincide when $m=2$. Members of the first famil
Externí odkaz:
http://arxiv.org/abs/2201.13253
Autor:
Allen, Michael A., Edwards, Kenneth
Publikováno v:
The Fibonacci Quarterly, vol. 61 (2023), no.1, pp. 21-27
The number of ways to tile an $n$-board (an $n\times1$ rectangular board) with $(\frac12,\frac12;1)$-, $(\frac12,\frac12;2)$-, and $(\frac12,\frac12;3)$-combs is $T_{n+2}^2$ where $T_n$ is the $n$th tribonacci number. A $(\frac12,\frac12;m)$-comb is
Externí odkaz:
http://arxiv.org/abs/2201.02285
Autor:
Allen, Michael P.
International Telemetering Conference Proceedings / October 25-28, 1993 / Riviera Hotel and Convention Center, Las Vegas, Nevada
Functional integration and validation of complex systems in an operational environment, prior to delivery or install
Functional integration and validation of complex systems in an operational environment, prior to delivery or install
Externí odkaz:
http://hdl.handle.net/10150/611853
http://arizona.openrepository.com/arizona/handle/10150/611853
http://arizona.openrepository.com/arizona/handle/10150/611853