We give a quadratic O(|X|) space representation based on a canonical tree for any subset family F ⊆ 2 holding the closure under union and difference of overlapping members. The cardinal of F is potentially in O(2), and its size higher. As far as we know this is the first representation theorem for such families. As an application of this framework we obtain a uniqueness decomposition theorem on...

We prove a decomposition theorem for the cd-index of a Gorenstein* poset analogous to the decomposition theorem for the intersection cohomology of a toric variety. From this we settle a conjecture of Stanley that the cd-index of Gorenstein* lattices is minimized on Boolean algebras.

Earlier work has shown that no extension of the Eckart–Young SVD approximation theorem can be made to the strong orthogonal rank tensor decomposition. Here, we present a counterexample to the extension of the Eckart–Young SVD approximation theorem to the orthogonal rank tensor decomposition, answering an open question previously posed by Kolda [SIAM J. Matrix Anal. Appl., 23 (2001), pp. 243–355].

We prove a new ‘runner removal theorem’ for q-decomposition numbers of the level 1 Fock space of typeA (1) e−1 , generalising earlier theorems of James–Mathas and the author. By combining this with another theorem relating to the Mullineux map, we show that the problem of finding all q-decomposition numbers indexed by partitions of a given weight is a finite computation.

We prove a conjecture of Denef on parameterized p-adic analytic integrals using an analytic cell decomposition theorem, which we also prove in this paper. This cell decomposition theorem describes piecewise the valuation of analytic functions (and more generally of subanalytic functions), the pieces being geometrically simple sets, called cells. We also classify subanalytic sets up to subanalyt...

In this paper, we prove that the Hodge-Laplace operator on strongly pseudoconvex compact complex Finsler manifolds is a self-adjoint elliptic operator. Then, from the decomposition theorem for self-adjoint elliptic operators, we obtain a Hodge decomposition theorem on strongly pseudoconvex compact complex Finsler manifolds. M.S.C. 2010: 53C56, 32Q99.

Finite type subshifts with finite number of symbols are important sort of discrete dynamical systems (often called symbolic dynamics) and are intensively studied [2, 3, 4, 5, 6]. Mañé proved a theorem (for finite type subshifts generated by 0, 1-square matrices), stating that topological transitivity and topological mixing can be reduced to algebraic properties of associated matrices [5]. In th...