A geometric perspective on counting non-negative integer solutions and combinatorial identities
نویسندگان
چکیده
منابع مشابه
features of short story in translated and non-translated literature: a polysystemic perspective
ترجمه متون ادبی در دنیای امروز از اهمیت ویژه ای برخوردار است. فرهنگ های مختلف با استفاده از متون ادبی ملل و فرهنگ های دیگر سعی در غنی کردن فرهنگ و ادبیات کشور خود دارند. کشور ما نیز از این قاعده مستثنی نیست. در ایران، ترجمه متون ادبی اروپائی که با دوران مشروطه ایرانی آغاز می شود موجب تغییرات اساسی در فرهنگ، شیوه زندگی و تفکر ایرانیان شده است. در این دوران نه تنها در امورات سیاسی و فکری کشور تغی...
15 صفحه اولHeat Traces on Spheres and Combinatorial Identities
Abstract. We present a concise explicit expression for the heat trace coefficients of spheres. Our formulas yield certain combinatorial identities which are proved following ideas of D. Zeilberger. In particular, these identities allow to recover in a surprising way some known formulas for the heat trace asymptotics. Our approach is based on a method for computation of heat invariants developed...
متن کاملOn Various Combinatorial Sums and Related Identities
In this talk we give a survey of results and methods on some combinatorial sums involving binomial coefficients and related to Bernoulli and Euler polynomials. We will also talk about certain sums of minima and maxima related to Dedekind sums. Some interesting identities associated with the various sums will also be introduced. 1. A curious identity and the sum ∑ k≡r (mod m) ( n k ) In 1988 Zhi...
متن کاملOn Chebyshev’s Polynomials and Certain Combinatorial Identities
Let Tn(x) and Un(x) be the Chebyshev’s polynomial of the first kind and second kind of degree n, respectively. For n ≥ 1, U2n−1(x) = 2Tn(x)Un−1(x) and U2n(x) = (−1)An(x)An(−x), whereAn(x) = 2n ∏n i=1(x− cos iθ), θ = 2π/(2n + 1). In this paper, we will study the polynomial An(x). Let An(x) = ∑n m=0 an,mx m. We prove that an,m = (−1)k2m ( l k ) , where k = bn−m 2 c and l = b 2 c. We also complete...
متن کاملCounting Solutions of Integer Programs Using Unrestricted Subtree Detection
In the recent years there has been tremendous progress in the development of algorithms to find optimal solutions for integer programs. In many applications it is, however, desirable (or even necessary) to generate all feasible solutions. Examples arise in the areas of hardware and software verification and discrete geometry. In this paper, we investigate how to extend branch-and-cut integer pr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Mathematical Education in Science and Technology
سال: 2014
ISSN: 0020-739X,1464-5211
DOI: 10.1080/0020739x.2014.985273