We study the posets (partially ordered sets) P, of partitions of an integer n, ordered by refinement, as defined by G. Birkhoff, “Lattice Theory” (3rd ed.) Colloq. Pub]. Vol. 25, 1967, Amer. Math. Sot. Providence. R.I. In particular we disprove the conjecture that the posets P,, are Cohen-Macaulay for all n. and show that even the Mobius function on the intervals does not alternate in sign in g...

Mobius coined the term "pathography", and since then, many practising doctors have used their clinical knowledge in attempting more fully to understand historical figures. The results are sometimes one-sided and smig, but ifused sensitively, as by Sir George Pickering or Lord Brain, the medical biography can be an exceptionally interesting historical exercise. William Ober belongs with the firs...

An interval edge t-coloring of a graph G is a proper edge coloring of G with colors 1,2...,t such that at least one edge of G is colored by color i,i=1,2...,t, and the edges incident with each vertex x are colored by d_{G}(x) consecutive colors, where d_{G}(x) is the degree of the vertex x in G. For Mobius ladders the existence of this coloring is proved and all possible numbers of colors in su...

i . Introduction How many probabi l i ty dis t r ibut ions can you th ink of wi th suppor t the unit disc? Th e uniform dis t r ibut ion probably comes to mind immediately. Th e only other dis t r ibut ions with suppor t the uni t disc tha t have any degree of familiari ty are the bivariate spherically symmetr ic be ta (or Pearson type II) dis t r ibut ions wi th densi ty (1.1) fir(x, y) = ~ (1...

The Murnaghan-Nakayama formula for the characters of Sn is derived from Young's seminormal representation, by a direct combinatorial argument. The main idea is a rational function identity which when stated in a more general form involves Mobius functions of posets whose Hasse diagrams have a planar embedding. These ideas are also used to give an elementary exposition of the main properties of ...

Standard Mobius transform evaluation formula for the Choquet integral is associated with the min-aggregation. However, several other aggregation operators replacing min operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all...

A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Mobius inversion and maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. The approach is illustrated on a simple example...

The synchrotron integrals used to compute emittances, the energy spread, etc., have been analyzed assuming no coupling between the horizontal and vertical planes[1, 2]. With Mobius, these assumptions are not valid and so this paper presents the appropriate generalizations. To simplify matters it will be still be assumed that the bends are in the horizonal plane. In this case I1, I2, I3, and I5 ...

This focus group study explored the social interaction experiences and strategies of 12 adults with Moebius Syndrome, a rare congenital condition characterized by facial paralysis. Content analysis revealed five themes of social functioning: social engagement/disengagement; resilience/sensitivity; social support/stigma; being understood/misunderstood; and public awareness/lack of awareness of M...