Results 61 to 70 of about 44,005 (262)

Some combinatorial identities concerning harmonic numbers and binomial coefficients [PDF]

Discrete Mathematics Letters, 2021
Dongwei Guo
doaj   +1 more source

Note on the binomial partial difference equation

Electronic Journal of Qualitative Theory of Differential Equations, 2015
Some formulas for the "general solution" to the binomial partial difference equation $$c_{m,n}=c_{m-1,n}+c_{m-1,n-1},$$ are known in the literature. However, it seems that there is no such a formula on the most natural domain connected to the equation ...
Stevo Stevic
doaj   +1 more source

Sum of the Reciprocals of the Binomial Coefficients

European Journal of Combinatorics, 1993
Let \(S_ n=\sum^ n_{k=0}{1 \over {n \choose k}}\). It is shown that \(S_ n\) satisfies the recurrence \(S_ n={n+1 \over 2n}S_{n-1}+1\). The proof can be simplified by observing that \[ n!S_ n=\sum^ n_{k=0}k!(n-k)!=n!+\sum^{n-1}_{k=0}k!(n-k-1)!(n+1-k-1) =n!+(n+ 1)(n-1)!S_{n-1}-(n!S_ n-n!). \]
openaire   +1 more source

Voluntary Collective Action to Address Growing Agricultural Challenges in Two Countries: Experimental Insights and Commonalities

Applied Economic Perspectives and Policy, EarlyView.
ABSTRACT We conducted two framed field economic experiments with citrus farmers in Florida, United States and soybean farmers in Argentina to investigate their willingness to coordinate pest and weed management efforts. Despite the contrast between these two agricultural contexts, we find striking behavioral commonalities.
Ariel Singerman, Sergio H. Lence
wiley   +1 more source

Generating Functions for New Families of Combinatorial Numbers and Polynomials: Approach to Poisson–Charlier Polynomials and Probability Distribution Function

Axioms, 2019
The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new ...
Irem Kucukoglu, Burcin Simsek, Yilmaz Simsek   +2 more
doaj   +1 more source

Harmonic number identities via polynomials with r-Lah coefficients

Comptes Rendus. Mathématique, 2020
In this paper, polynomials whose coefficients involve $r$-Lah numbers are used to evaluate several summation formulae involving binomial coefficients, Stirling numbers, harmonic or hyperharmonic numbers.
Kargın, Levent, Can, Mümün
doaj   +1 more source

Agricultural Diversification at the Margin. Strategies and Determinants in Italian Mountain and Remote Areas

Agribusiness, EarlyView.
ABSTRACT This paper explores the convergence in on‐farm diversification strategies of agricultural holdings, between remote areas and more central ones. Using Italian farm‐level data, we explore the determinants of diversification strategies across farms.
Gianluca Grilli, Francesco Pagliacci, Paola Gatto   +2 more
wiley   +1 more source

Livelihood Diversification as an Adaptation Strategy to Climate Change and Household Food Security of Livestock Holders in Pakistan

Agribusiness, EarlyView.
ABSTRACT Rural farm households continue to face significant risks from climate change, resulting in many of them diversifying their livelihood sources into other income‐generating activities to increase their incomes and improve food and nutrition security. In this study, we examine the drivers and impact of farm households' participation in livelihood
Mahwish Arshad, Awudu Abdulai
wiley   +1 more source

A divisibility property of binomial coefficients viewed as an elementary sieve

International Journal of Mathematics and Mathematical Sciences, 1981
The triangular array of binomial coefficients 012301111212131331… is said to have undergone a j-shift if the r-th row of the triangle is shifted rj units to the right (r=0,1,2,…). Mann and Shanks have proved that in a 2-shifted array a column number c>
Richard H. Hudson, Kenneth S. Williams
doaj   +1 more source

Combinatorial representation of the sum of the weighted equal powers of members of an arithmetical progression

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013
The correctness of equality which gives the combinatorial expression for the sum of the weighted equal powers of members of an arithmetical progression is found out.
Alexander I Nikonov
doaj   +1 more source