We prove that the number of cyclically symmetric, self-complementary plane partitions contained in a cube of side 2n equals the square of the number of totally symmetric, self-complementary plane partitions contained in the same cube, without explicitly evaluating either of these numbers. This appears to be the first direct proof of this fact. The problem of finding such a proof was suggested b...

The transportation of petroleum represents one of the most strategically important circulations of resources in the global economy. Its role cannot be overstated. Yet, petroleum has become a “strategically invisible” commodity as its flow has been continuous with limited, but eye-opening, disruptions such as the First Energy Crisis is 1973. Petroleum supplies are virtually taken for granted. Si...

In this paper we settle a weak version of a conjecture (i.e. Conjecture 6) by Mills, Robbins and Rumsey in the paper “Self-complementary totally symmetric plane partitions” J. Combin. Theory Ser. A 42, 277–292. In other words we show that the number of shifted plane partitions invariant under the involution γ is equal to the number of alternating sign matrices invariant under the vertical flip....

Conventionally, the design of linear-phase 2-D FIR digital filters is concentrated on the class of quadrantally symmetric filters, such as circular filters, fan-type filters etc [l]. A 2-D sequence, which is symmetric in both directions, is required to realize such quadrantally symmetric filters. In this paper, we will start from the discussion of the symmetric properties of 2-D sequences to di...

We perform Langevin dynamic numerical simulation on a double-well potential system subjected to an asymmetric saw-tooth type external time varying field and white noise forces. The hysteresis loss calculated from the first-passage time distribution obtained shows asymmetric behaviour with respect to the asymmetry in the field sweep. The hysteresis loss, in our model, being a measure of the sync...

We have investigated the in-plane anisotropy of c-axis magnetoresistance (MR) in both superconducting and normal states single crystals NdO0.7F0.3BiS2 under magnetic fields. In NdO0.7F0.3BiS2, four-fold-symmetric MR was observed below transition temperature. Since crystal structure is tetragonal, rotational symmetry state preserved present compound. This result clearly different from previous r...

We present multiresidue integral formulae for partial sums in the basis of link patterns of the polynomial solution to the level 1 Uq(ŝl2) quantum Knizhnik–Zamolodchikov equation at generic values of the quantum parameter q. These allow for rewriting and generalizing a recent conjecture [Di Francesco ’06] connecting the above to generating polynomials for weighted Totally Symmetric Self-Complem...

In this paper we show that the existence of plane partitions, which are minimal in a sense to be defined, yields minimal irreducible summands in the Kronecker product χ ⊗ χ of two irreducible characters of the symmetric group S(n). The minimality of the summands refers to the dominance order of partitions of n. The multiplicity of a minimal summand χ equals the number of pairs of Littlewood-Ric...