We give a basis for the space spanned by the sumˆs λ of the lowest degree terms in the expansion of the Schur symmetric functions s λ in terms of the power sum symmetric functions p µ , where deg(p i) = 1. These lowest degree terms correspond to minimal border strip tableaux of λ. The dimension of the space spanned byˆs λ , where λ is a partition of n, is equal to the number of partitions of n ...

This paper presents a two-stage low-noise ultra-wideband amplifier to obtain high and smooth gain in 180nm CMOS Technology. The proposed structure has two common source stages with inductive feedback. First stage is designed about 3GHz frequency and second stage is designed about 8GHz. In simulation, symmetric inductors of TSMC 0.18um CMOS technology in ADS software is used.Simulations results ...

In this paper we propose a new method for applying hiding countermeasure against CPA attacks. This method is for software implementation, based on smoothing power consumption of the device. This method is evaluated on the SIMON scheme as a case study; however, it is not relying on any specific SIMON features. Our new method includes only AND equivalent and XOR equivalent operations since every ...

In this note we classify when a skew Schur function is a positive linear combination of power sum symmetric functions. We then use this to determine precisely when any scalar multiple of a skew Schur function is the chromatic symmetric function of some graph. As a consequence we prove that of the classical bases for symmetric functions only certain scalar multiples of the elementary symmetric f...

In ad-hoc wireless networks, certain network connectivity constraints are of interest because of their practical importance. An example of such a constraint would be strong connectivity. The aim is usually to minimize the power used to maintain such connectivities by adjusting the transmission power of the nodes of the network. Such problems are called Power Assignment problems. Another set of ...

We consider a cyclic group of order p acting on a module incharacteristic p and show how to reduce the calculation of the symmetric algebra to that of the exterior algebra. Consider a cyclic group of order p acting on a polynomial ring S = k[x1, . . . , xr], where k is a field of characteristic p; this is equivalent to the symmetric algebra S∗(V ) on the module V generated by x1, . . . , xr. We...

This paper presents a formula for products of Schubert classes in the quantum cohomology ring of the Grassmannian. We introduce a generalization of Schur symmetric polynomials for shapes that are naturally embedded in a torus. Then we show that the coefficients in the expansion of these toric Schur polynomials, in terms of the regular Schur polynomials, are exactly the 3-point Gromov-Witten inv...

Let V be an n-dimensional vector space. We give a direct construction of an exact sequence that gives a GL(V)-equivariant " resolution " of each symmetric power S t V in terms of direct sums of tensor products of the form ∧ i 1 V ⊗ · · · ⊗ ∧ ip V. This exact sequence corresponds to inverting the relation in the representation ring of GL(V) that is described by the Koszul complex, and has appear...

We show that the directed st-connectivity problem cannot be expressed in symmetric Datalog, a fragment of Datalog introduced in [5]. It was shown there that symmetric Datalog programs can be evaluated in logarithmic space and that this fragment of Datalog captures logspace when augmented with negation, and an auxiliary successor relation S together with two constant symbols for the smallest and...

Let C be a smooth projective absolutely irreducible curve of genus g ≥ 2 over a number field K, and denote its Jacobian by J . Let d ≥ 1 be an integer and denote the d-th symmetric power of C by C(d). In this paper we adapt the classic Chabauty–Coleman method to study the K-rational points of C(d). Suppose that J(K) has Mordell–Weil rank at most g− d. We give an explicit and practical criterion...