Triangle-Free Triangulations, Hyperplane Arrangements and Shifted Tableaux

Flips of diagonals in colored triangle-free triangulations of a convex polygon are interpreted as moves between two adjacent chambers in a certain graphic hyperplane arrangement. Properties of geodesics in the associated flip graph are deduced. In particular, it is shown that: (1) every diagonal is flipped exactly once in a geodesic between distinguished pairs of antipodes; (2) the number of geodesics between these antipodes is equal to twice the number of Young tableaux of a truncated shifted staircase shape.Comment: figure added, plus several minor change

ANALISA KERUSAKAN DIES HAMMER FORGING MATERIAL SKT4 UNTUK PROSES PRODUKSI UNDER BRACKET

Forging merupakan salah satu proses pengerjaan logam yang dilakukan dengan cara merbah bentuk material logam  dengan memberikan gaya tekan melalui  cetakan die sampai terjadi deformasi plastis pada material. Gaya tekan akan merubah bentuk serta dimensi benda kerja secara permanent mengikuti profil yang ada pada cetakan.Faktor yang melatar belakangi terjadinya kerusakan pada dies dipengaruhi oleh gaya dan tegangan yang bekerja, serta struktur dan kekerasan material dies tersebut. Dilakukan pengujian untuk memastikan penyebab kerusakan, meliputi pengujian struktur mikro,komposisi kimia, dan uji kekerasan. Hasil pengujian diperoleh bahwa kerusakan dies, disebabkan adanya material las pada dies. Selain gaya dan tegangan serta pembebanan yang berlebih. Awal kerusakan berada pada material dies yang berhubungan langsung dengan beban statis dan terdapat material las di bagian tersebut

On Degrees in the Hasse Diagram of the Strong Bruhat Order

For a permutation $\pi$ in the symmetric group $S_n$ let the {\it total degree} be its valency in the Hasse diagram of the strong Bruhat order on $S_n$, and let the {\it down degree} be the number of permutations which are covered by $\pi$ in the strong Bruhat order. The maxima of the total degree and the down degree and their values at a random permutation are computed. Proofs involve variants of a classical theorem of Tur\'an from extremal graph theory.Comment: 14 pages, minor corrections; to appear in S\'em. Lothar. Combi

Shape Avoiding Permutations

Permutations avoiding all patterns of a given shape (in the sense of Robinson-Schensted-Knuth) are considered. We show that the shapes of all such permutations are contained in a suitable thick hook, and deduce an exponential growth rate for their number.Comment: 16 pages; final form, to appear in J. Combin. Theory, Series

Equidistribution and Sign-Balance on 321-Avoiding Permutations

Let $T_n$ be the set of 321-avoiding permutations of order $n$. Two properties of $T_n$ are proved: (1) The {\em last descent} and {\em last index minus one} statistics are equidistributed over $T_n$, and also over subsets of permutations whose inverse has an (almost) prescribed descent set. An analogous result holds for Dyck paths. (2) The sign-and-last-descent enumerators for $T_{2n}$ and $T_{2n+1}$ are essentially equal to the last-descent enumerator for $T_n$. The proofs use a recursion formula for an appropriate multivariate generating function.Comment: 17 pages; to appear in S\'em. Lothar. Combi

Enumeration of Standard Young Tableaux

A survey paper, to appear as a chapter in a forthcoming Handbook on Enumeration.Comment: 65 pages, small correction

The Diabetic Dog as a Translational Model for Human Islet Transplantation.

The dog model has served as the primary method for early development of many diabetes therapies, including pancreatic islet transplantation techniques and immunosuppressive protocols. Recent trends towards the use of monoclonal antibody therapies for immunosuppression in human islet transplantation have led to the increasing use of primate models with induced diabetes. In addition to induced-disease models in large animals, scientists in many fields are considering the use of naturally-occurring disease models in client-owned pets. This article will review the applicability of naturally-occurring diabetes in dogs as a translational model for developing islet transplantation in the human diabetic patient