共查询到19条相似文献,搜索用时 46 毫秒
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一类与多项式相关的组合恒等式 总被引:5,自引:1,他引:4
一类与多项式相关的组合恒等式王良成(四川省达县师专635000)本文给出一类与多项式相关的组合恒等式,由此可以产生许多有用的组合恒等式.定理设是1+1次多项式,则证明1°当n-1,即f(x)=ax2+bx+c0时,则即(1)式成立.2°假设n=k,即... 相似文献
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二类有趣的组合恒等式湖南岳阳师专肖振纲在拙文[1]中,我们证明了如下的(即原文引理2)引理数列a0,a1,…,an(n≥2)成等差数列的充分必要条件为:对任意整数i,当1≤i≤n—1时,恒有并由此给出了二项式定理的一个推广.本文继续在此引理的基础上,... 相似文献
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The authors show that certain theta function identities of Schroeter and Ramanujan imply elegant partition identities. 相似文献
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两个三角函数恒等式及其应用 总被引:1,自引:0,他引:1
定理 1 设α ,β ,γ∈R ,则有cosαsin(β -γ) cosβsin(γ -α) cosγsin(α - β) =0 . (1) 定理 2 设α ,β ,γ∈R ,则有sinαsin(β -γ) sinβsin( γ -α) sinγsin(α - β) =0 .(2 )证 构造二元一次方程组xcosα ycosβ =cosγxsinα ysinβ =sinγ(3)(4 )由 (3) ,(4 )两式可得 xsin(α - β) =sin(γ - β) (5) ysin(α - β) =sin(α -γ) (6 )将 (3)式两边同乘sin(α - β)后 ,再将 (5) ,(6 )两式代入即得定理 1.将 (4 )式… 相似文献
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本文利用初等刀法简捷地推广了Paule的结果,从而得到了一系列多重Rogers-Ramanujan恒等式. 相似文献
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利用一个基本超几何函数的变换公式及其最基本的求和公式,对Gessel I.和Stanton D。发现的两个Rogers-Ramanujan恒等式,给出一种新的、更为简单的证明。 相似文献
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《代数通讯》2013,41(4):1011-1022
ABSTRACT The algebras M a, b (E) ? E and M a+b (E) are PI equivalent over a field of characteristic 0 where E is the infinite-dimensional Grassmann algebra. This result is a part of the well-known tensor product theorem. It was first proved by Kemer in 1984–1987 (see Kemer 1991); other proofs of it were given by Regev (1990), and in several particular cases, by Di Vincenzo (1992), and by the authors (2004). Using graded polynomial identities, we obtain a new elementary proof of this fact and show that it fails for the T-ideals of the algebras M 1, 1(E) ? E and M 2(E) when the base field is infinite and of characteristic p > 2. The algebra M a, a (E) ? E satisfies certain graded identities that are not satisfied by M 2a (E). In another paper we proved that the algebras M 1, 1(E) and E ? E are not PI equivalent in positive characteristic, while they do satisfy the same multilinear identities. 相似文献
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Allan Berele 《代数通讯》2013,41(12):5338-5347
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q-Analogues of the coefficients of xa in the expansion of
j=1
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(1 + x + + xj)Lj are proposed. Useful properties, such as recursion relations, symmetries and limiting theorems of the q-supernomial coefficients are derived, and a combinatorial interpretation using generalized Durfee dissection partitions is given. Polynomial identities of boson-fermion-type, based on the continued fraction expansion of p/k and involving the q-supernomial coefficients, are proven. These include polynomial analogues of the Andrews-Gordon identities. Our identities unify and extend many of the known boson-fermion identities for one-dimensional configuration sums of solvable lattice models, by introducing multiple finitization parameters. 相似文献
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We present three infinite families of partitions that, for corresponding parameters, are equinumerous. This generalizes an identity proved by the first author (Pacific Journal of Mathematics, 77(1) (1978)) and two identities proved by the second and third authors (Relatório Técnico
08/99 IMECC-UNICAMP, 1999). 相似文献
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初文昌 《纯粹数学与应用数学》1993,9(1):1-6
本文提出联系两类组合恒等式的极限方法,据此可二项式系数和项式系数恒等式自然过渡到Abel型系数的组合等式。因此对任一给定的含参量的二项式系数的组合恒等式。这一方法可用于直接证明其至发现相同结构的Abel系数恒等式。 相似文献
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Plamen Koshlukov 《代数通讯》2013,41(7):3095-3113
Let L be a Lie algebra, nilpotent of class 2, over an infinite field K, and suppose that the centre C of L is one dimensional; such Lie algebras are called Heisenberg algebras. Let ρ:L→hom KV be a finite dimensional representation of the Heisenberg algebra L such that ρ(C) contains non-singular linear transformations of V, and denote l(ρ) the ideal of identities for the representation ρ. We prove that the ideals of identities of representations containing I(ρ) and generated by multilinear polynomials satisfy the ACC. Let sl 2(L) be the Lie algebra of the traceless 2×2 matrices over K, and suppose the characteristic of K equals 2. As a corollary we obtain that the ideals of identities of representations of Lie algebras containing that of the regular representation of sl 2(K) and generated by multilinear polynomials, are finitely based. In addition we show that one cannot simply dispense with the condition of multilinearity. Namely, we show that the ACC is violated for the ideals of representations of Lie algebras (over an infinite field of characteristic 2) that contain the identities of the regular representation of sl 2(K). 相似文献
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David P. Little 《Journal of Combinatorial Theory, Series A》2009,116(1):223-231
In 1840, V.A. Lebesgue proved the following two series-product identities:
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In this paper we present a new infinite family of partition identities. The genesis of our work lies in two formulas of Lucy Slater related to the modulus 8. Hirschhorn, Agarwal and Subbarao have previously found intriguing interpretations for Slater's formula, but none has led to an infinite family of results. 相似文献