Abstract. We give a new description of the flag major index, introduced by Adin and Roichman, by using a major index defined by Reiner. This allows us to establish a connection between an identity of Reiner and some more recent results due to Chow and Gessel. Furthermore we generalize the main identity of Chow and Gessel by computing the four-variate generating series of descents, major index, ...

Adin, Brenti, and Roichman introduced the pairs of statistics (ndes, nmaj) and (fdes, fmaj). They showed that these pairs are equidistributed over the hyperoctahedral group B n , and can be considered " Euler-Mahonian " in that they generalize the Carlitz identity. Further, they asked whether there exists a bijective proof of the equidistribution of their statistics. We give such a bijection, a...

Figuring out the non-genetic factors that heighten the risk of Alzheimer’s disease is especially challenging, and the recent study is one step in a long process of looking at the effects of stress and other environmental factors, according to Golde. It could also point the way to a novel treatment approach in the future, he said. UF Health Researchers Find Some Evidence of Link Between Stress, ...

Adin, Brenti, and Roichman introduced the pairs of statistics (ndes, nmaj) and (fdes, fmaj). They showed that these pairs are equidistributed over the hyperoctahedral group Bn, and can be considered “Euler-Mahonian” in that they generalize the Carlitz identity. Further, they asked whether there exists a bijective proof of the equidistribution of their statistics. We give such a bijection, along...

We give a new description of the flag major index, introduced by Adin and Roichman, by using a major index defined by Reiner. This allows us to establish a connection between an identity of Reiner and some more recent results due to Chow and Gessel. Furthermore we generalize the main identity of Chow and Gessel by computing the four-variate generating series of descents, major index, length, an...

By JAMES C. ALEXANDER, ANDREW J. BERNOFF, ELIZABETH K. MANN, J. ADIN MANN Jr, JACOB R. WINTERSMITH AND LU ZOU Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA Department of Physics, Kent State University, Kent, OH 44242, USA Department of Chemical Engineering, Case Western Reserve Univer...

A ntibodies protect against lethal infection by bacteria or nonenveloped viruses such as adenovirus (1). They are secreted by plasma cells at the rate of thousands of molecules per second, and it has long been assumed that they function exclusively in the extracellular milieu. The recent discovery of a cytoplasmic process called antibody-dependent intracellular neutralization (ADIN) put an end ...

We introduce the cyclic major index of a permutation and give bivariate analogue enumerative formula for shuffles with given descent number due to Adin, Gessel, Reiner Roichman, which can be viewed as Stanley's shuffling theorem. This gives an answer question has been posed by Domagalski, Liang, Minnich, Sagan, Schmidt Sietsema again.

one of the tragic consequences of the great wars is the spread of epi-demics. at the end of the first world war, flu spread in europe and soon spread in many parts of the world including iran. this event was accompanied by loss of many people in shiraz. in two notes remained from that time, one belongs to a liberal  and the other one belongs to one of the most famous physicians of shiraz, the o...

We introduce a natural extension of Adin, Brenti, and Roichman’s major-index statistic nmaj on signed permutations (Adv. Appl. Math. 27, (2001), 210−244) to wreath products of a cyclic group with the symmetric group. We derive “insertion lemmas” which allow us to give simple bijective proofs that our extension has the same distribution as another statistic on wreath products introduced by Adin ...