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- Catalan number (2)
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- Newsboy Problem; Inventory and Revenue Management; Optimization (1)
- Recurrence (1)
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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
On The Least Significant P-Adic Digits Of Certain Lucas Numbers, Tamas Lengyel
On The Least Significant P-Adic Digits Of Certain Lucas Numbers, Tamas Lengyel
Tamas Lengyel
We calculate the least significant p-ary digits of certain Lucas numbers Vn = Vn(P,Q)withV0 =2,V1 =PandVn =PVn1QVn2 forn2. Webase our study on an observation regarding these numbers: as m increases, more and more p-adic digits match in Vkpm with integer k 1. We use multi-section identities for generating functions and derive congruences for the underlying sequences.
On The Least Significant 2-Adic And Ternary Digits Of Certain Stirling Numbers, Tamas Lengyel
On The Least Significant 2-Adic And Ternary Digits Of Certain Stirling Numbers, Tamas Lengyel
Tamas Lengyel
Our main goal is to effectively calculate the p-ary digits of certain Stirling numbers of the second kind. We base our study on an observation regarding these numbers: as m increases, more and more p-adic digits match in S(i(p − 1)pm, k) with integer i ≥ 1.
On Divisibility Properties Of Some Differences Of The Central Binomial Coefficients And Catalan Numbers, Tamas Lengyel
On Divisibility Properties Of Some Differences Of The Central Binomial Coefficients And Catalan Numbers, Tamas Lengyel
Tamas Lengyel
We discuss divisibility properties of some differences of the central binomial coeffi- cients and Catalan numbers. The main tool is the application of various congruences modulo high prime powers for binomial coefficients combined with some recurrences relevant to these combinatorial quantities.
Revisiting The Newsboy Problem-Optimization With A Little Help From The Airline Industry, Tamas Lengyel
Revisiting The Newsboy Problem-Optimization With A Little Help From The Airline Industry, Tamas Lengyel
Tamas Lengyel
In a typical inventory planning problem with a life cycle of only one planning period, we incur the cost of production per unit produced, profit per unit sold, loss per unit not sold, and lost revenue per unit ordered but not matched due to the lack of availability. The goal is to find the inventory level that maximizes the expected net profit. Textbooks often use the newsboy problem to illustrate the inventory management paradigm. The derivation of the formulas for the optimal level is usually done on an ad hoc basis, by dull and rote mathematical manipulations, for each modification …
On Divisibility Properties Of Some Differences Of Motzkin Numbers, Tamas Lengyel
On Divisibility Properties Of Some Differences Of Motzkin Numbers, Tamas Lengyel
Tamas Lengyel
We discuss divisibility properties of some differences of Motzkin numbers Mn. The main tool is the application of various congruences of high prime power moduli for binomial coefficients and Catalan numbers combined with some recurrence relevant to these combinatorial quantities and the use of infinite disjoint covering systems. We find proofs of the fact that, for different settings of a and b, more and more p-ary digits of Mapn+1+b and Mapn+b agree as n grows.
Note On The Unbiased Estimation Of A Function Of The Parameter Of The Geometric Distribution, Tamas Lengyel
Note On The Unbiased Estimation Of A Function Of The Parameter Of The Geometric Distribution, Tamas Lengyel
Tamas Lengyel
Kolmogorov studied the problem of whether a function of the parameter p of the Bernoulli distribution Bernoulli[p] has an unbiased estimator based on a sample X1,X2,...,Xn of size n and proved that exactly the polynomial functions of degree at most n can be estimated. For the geometric distribution Geometric[p], we prove that exactly the functions that are analytic at p = 1 have unbiased estimators and present the best estimators.
On Some 2-Adic Properties Of A Recurrence Involving Stirling Numbers, Tamas Lengyel
On Some 2-Adic Properties Of A Recurrence Involving Stirling Numbers, Tamas Lengyel
Tamas Lengyel
We analyze some 2 adic properties of the sequence defined by the recurrence Z(1) =1; Z(n) = n−1 k=1 S(n, k) Z(k), n ≥ 2, which counts the number of ultra-dissimilarity relations, i.e., ultra-metrics on an n-set. We prove the 2 adic growth property v2 (Z(n) ≥ log 2 n - 1) and present conjectures on the exact values.
Direct Consequences Of The Basic Ballot Theorem, Tamas Lengyel
Direct Consequences Of The Basic Ballot Theorem, Tamas Lengyel
Tamas Lengyel
We use only the classic basic ballot result and simple combinatorial arguments to derive the distributions of the first passage time and the number of visits in the usual random walk model.
On Approximating Point Spread Distributions, Tamas Lengyel
On Approximating Point Spread Distributions, Tamas Lengyel
Tamas Lengyel
We discuss some properties of the point spread distribution, defined as the distribution of the difference of two independent binomial random variables with the same parameter n in- cluding exact and approximate probabilities and related optimization issues. We use various approximation techniques for different distributions, special functions, and analytic, combi- natorial and symbolic methods, such as multi-summation techniques. We prove that in case of unequal success rates, if these rates change with their difference kept fix and small, and n is appropriately bounded, then the point spread distribution only slightly changes for small point differences. We also prove that for …