This paper finds and analyzes a formula for the total variation distance between iterations of riffle shuffles and iterations of “cut and then riffle shuffle”. This allows one to obtain information about the convergence rate of permutation statistics (such as the length of the longest increasing subsequence or position of a given card) under these processes. Similar results are given for affine...

Abstract. We compute the limit distribution for (centered and scaled) length of the longest increasing subsequence of random colored permutations. The limit distribution function is a power of that for usual random permutations computed recently by Baik, Deift, and Johansson (math.CO/9810105). In two–colored case our method provides a different proof of a similar result by Tracy and Widom about...

We prove a formula for the number of permutations in Sn such that their first n−k entries are increasing and their longest increasing subsequence has length n − k. This formula first appeared as a consequence of character polynomial calculations in the work of Adriano Garsia, [2]. We give an elementary proof of this result and also of its q-analogue. In [2], Adriano Garsia derived as a conseque...

Protected areas (PAs) have long been criticized as creations of and for an elite few, where associated costs, but few benefits, are borne by marginalized rural communities. Contrary to predictions of this argument, we found that average human population growth rates on the borders of 306 PAs in 45 countries in Africa and Latin America were nearly double average rural growth, suggesting that PAs...

in the turfgrass industry, the need for salinity tolerant turfgrasses is increasing because of the increased use of saline and non-potable water. greenhouse container experiments were conducted to determine the relative salinity tolerance and growth responses of eleven native populations of tall fescue (festuca arundinacea schrub) (tf), including: semirom, mashhad, sanandaj, yasuj, yazd abad, d...

nowadays, population growth and on the other hand resources limitations astonish authorities. population changes cause variation in economic activities and land use changes. as a whole, overusing, improper land use and human disturbances over natural resources make environmental imbalances worse. in recent decades, we have seen land use changes in taleghan basin. land use changes were produced ...