A simple optimal binary representation of mosaic floor plans and Baxter permutations

Mosaic floorplans are rectangular structures subdivided into smaller rectangular sections and are widely used in VLSI circuit design. Baxter permutations are a set of permutations that have been shown to have a one-to-one correspondence to objects in the Baxter combinatorial family, which includes mosaic floorplans. An important problem in this area is to find short binary string representations of the set of n-block mosaic floorplans and Baxter permutations of length n. The best known representation is the Quarter-State Sequence which uses 4n bits. This paper introduces a simple binary representation of n-block mosaic floorplan using 3n−3 bits. It has been shown that any binary representation of n-block mosaic floorplans must use at least (3n−o(n)) bits. Therefore, the representation presented in this paper is optimal (up to an additive lower order term)

Exceptional and Anisotropic Transport Properties of Photocarriers in Black Phosphorus

We show that black phosphorus has room-temperature charge mobilities on the order of 10$^4$ cm$^2$V$^{-1}$s$^{-1}$, which are about one order of magnitude larger than silicon. We also demonstrate strong anisotropic transport in black phosphorus, where the mobilities along the armchair direction are about one order of magnitude larger than zigzag direction. A photocarrier lifetime as long as 100 ps is also determined. These results illustrate that black phosphorus is a promising candidate for future electronic and optoelectronic applications.Comment: 5 pages, 4 figure

A conjecture on the number of SDRs of a (t,n)-family

AbstractA system of distinct representatives (SDR) of a family F=(A1,…,An) is a sequence (x1,…,xn) of n distinct elements with xi∈Ai for 1≤i≤n. Let N(F) denote the number of SDRs of a family F; two SDRs are considered distinct if they are different in at least one component. For a nonnegative integer t, a family F=(A1,…,An) is called a (t,n)-family if the union of any k≥1 sets in the family contains at least k+t elements. The famous Hall’s theorem says that N(F)≥1 if and only if F is a (0,n)-family. Denote by M(t,n) the minimum number of SDRs in a (t,n)-family. The problem of determining M(t,n) and those families containing exactly M(t,n) SDRs was first raised by Chang [G.J. Chang, On the number of SDR of a (t,n)-family, European J. Combin. 10 (1989) 231–234]. He solved the cases when 0≤t≤2 and gave a conjecture for t≥3. In this paper, we solve the conjecture