We provide a characterization of the obligation rules in the context of minimum cost spanning tree games. We also explore the relation between obligation rules and random order values of the irreducible cost game it is shown that the later is a subset of the obligation rules. Moreover we provide a necessary and sufficient condition on obligation function such that the corresponding obligation r...

As is well known, the Schur complements of strictly or irreducibly diagonally dominant matrices are H−matrices; however, the same is not true of generally diagonally dominant matrices. This paper proposes some conditions on the generally diagonally dominant matrix A and the subset α ⊂ {1, 2, . . . , n} so that the Schur complement matrix A/α is an H−matrix. These conditions are then applied to ...

Let A be a subset of the polynomials of degree less than N over a finite field Fq. Let r be any non-zero element of Fq. We show that if the difference set A−A does not contain elements of the form P + r, where P is a monic, irreducible polynomial, then |A| ≤ Cq N log N , where C and c are constants depending only on q.

Suppose that G(F) is a real or p-adic group. That is, G is a connected reductive algebraic group over a local field F, which we take to be of characteristic 0. Harmonic analysis on G(F) is built upon the set Htemp(G(F)) of irreducible tempered representations of G(F). These representations include the discrete series for G(F), and consist in general of irreducible constituents of representation...

We prove that a minimal isometric immersion of a Kähler-Einstein or homogeneous Kähler manifold into an Euclidean space must be totally geodesic. As an application we show that an open subset of the real hyperbolic plane RH2 cannot be minimally immersed into the Euclidean space. As another application we prove that if an irreducible Kähler manifold is minimally immersed in an Euclidean space th...

We present a construction of constant weight codes based on the unique decomposition of elements in lattices. The conditions for unique primary decomposition and unique irreducible decomposition in lattices are discussed and the connections with decomposition of ideals in Noetherian commutative rings established. The source alphabet in our proposed construction is a set of uniquely decomposable...

Let ∆ ( V be a proper subset of the vertices V of the defining graph of an irreducible and aperiodic shift of finite type (Σ+A, T ). Let ∆n be the union of cylinders in Σ + A corresponding to the points x for which the first n-symbols of x belong to ∆ and let μ be an equilibrium state of a Hölder potential φ on Σ+A. We know that μ(∆n) converges to zero as n diverges. We study the asymptotic beh...

We study the Spohn conditional independence (CI) variety CX of an n-player game X for undirected graphical models on n binary random variables consisting one edge. For a generic game, we show that is smooth irreducible complete intersection curve (Nash curve) in Segre (P1)n−2×P3 and give explicit formula its degree genus. prove two universality theorems CX: The product any affine real algebraic...

Let Φ be an irreducible root system (sometimes we denote Φ by Φ(X) to indicate its type X). Choose a simple root system Π in Φ. Let Φ + (resp. Φ~) be the corresponding positive (resp. negative) root system of Φ. By a subsystem Φ' of Φ (resp. of Φ + ) , we mean that Φ' is a subset of Φ (resp. of Φ) which itself forms a root system (resp. a positive root system). We refer the readers to Bourbaki'...

We introduce the matroid-minor coalgebra C, which has labeled matroids as distinguished basis, and coproduct given by splitting a matroid into a submatroid and complementary contraction all possible ways. We introduce two new bases for C; the first of these is is related to the distinguished basis by Möbius inversion over the rank-preserving weak order on matroids, the second by Möbius inversio...