Congruences modulo powers of 5 for k -colored partitions
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2017.10.027
Abstract: Let $p_{-k}(n)$ enumerate the number of $k$-colored partitions of $n$. In this paper, we establish some infinite families of congruences modulo 25 for $k$-colored partitions. Furthermore, we prove some infinite families of Ramanujan-type congruences modulo… read more here.
Keywords: align; modulo powers; powers colored; colored partitions ... See more keywords
Proof of some conjectural congruences involving Apéry-like sequences
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Difference Equations and Applications"
DOI: 10.1080/10236198.2024.2446458
Abstract: In this paper, we evaluate $$\begin{align*} \sum_{k=1}^{p-1}\frac1{k^3}\binom{x}k\binom{-1-x}k\quad \mbox{and}\quad \sum_{k=1}^{p-1}\frac1{k^2}\binom{x}k\binom{-1-x}k \end{align*}$$∑k=1p−11k3(xk)(−1−xk)and∑k=1p−11k2(xk)(−1−xk) modulo p and modulo $ p^2 $ p2 respectively, and by these we prove some conjectures of Z.-H. Sun involving $$\begin{align*} V_n(x)=\sum_{k=0}^n\binom{n}k\binom{n+k}k(-1)^k\binom{x}k\binom{-1-x}k \end{align*}$$Vn(x)=∑k=0n(nk)(n+kk)(−1)k(xk)(−1−xk) with n = p,… read more here.
Keywords: proof conjectural; congruences involving; align; conjectural congruences ... See more keywords
A Process Evaluation of a Palliative Care Social Work Intervention for Cancer Patients in Skilled Nursing Facilities
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Palliative Medicine"
DOI: 10.1089/jpm.2023.0381
Abstract: Background: Assessing and Listening to Individual Goals and Needs (ALIGN) is a palliative care social work intervention that aims to improve delivery of goal-concordant care for hospitalized older adults with cancer discharged to skilled nursing… read more here.
Keywords: social work; care social; care; align ... See more keywords
LS‐align: an atom‐level, flexible ligand structural alignment algorithm for high‐throughput virtual screening
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DOI: 10.1093/bioinformatics/bty081
Abstract: Motivation Sequence‐order independent structural comparison, also called structural alignment, of small ligand molecules is often needed for computer‐aided virtual drug screening. Although many ligand structure alignment programs are proposed, most of them build the alignments… read more here.
Keywords: virtual screening; ligand; structural alignment; align ... See more keywords
An Elekes–Rónyai Theorem for Sets With Few Products
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DOI: 10.1093/imrn/rnae087
Abstract: Given $n \in \mathbb{N}$, we call a polynomial $F \in \mathbb{C}[x_{1},\dots ,x_{n}]$ degenerate if there exist $P\in \mathbb{C}[y_{1}, \dots , y_{n-1}]$ and monomials $m_{1}, \dots , m_{n-1}$ with fractional exponents, such that $F = P(m_{1},… read more here.
Keywords: mathbb; elekes nyai; nyai theorem; sets products ... See more keywords
Weakly Divisible Rings
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DOI: 10.1093/imrn/rnaf166
Abstract: We define a new class of rings parameterized by binary forms of a certain type and give an effective lower bound for the number of such rings whose discriminant is less than a bound $X$.… read more here.
Keywords: number; frac frac; discriminant less; frac ... See more keywords