Multi-Schur functions are symmetric that generalize the supersymmetric Schur functions, flagged and refined dual Grothendieck which have been intensively studied by Lascoux. In this paper, we give a new free-fermionic presentation of them. The multi-Schur indexed partition two ``tuples tuples'' indeterminates. We construct family linear bases fermionic Fock space such data prove they correspond...

We use Hopf algebras to prove a version of the Littlewood–Richardson rule for skew Schur functions, which implies a conjecture of Assaf and McNamara. We also establish skew Littlewood–Richardson rules for Schur P and Q-functions and noncommutative ribbon Schur functions, as well as skew Pieri rules for k-Schur functions, dual k-Schur functions, and for the homology of the affine Grassmannian of...

We introduce fusion bialgebras and their duals systematically study Fourier analysis. As an application, we discover new efficient analytic obstructions on the unitary categorification of rings. prove Hausdorff-Young inequality, uncertainty principles for duals. show that Schur product property, Young's inequality sum-set estimate hold bialgebras, but not always If ring is Grothendieck a catego...

Motivated by the Q-property of nonsingular M-matrices, Lyapunov and Stein transformations (corresponding to positive stable and Schur stable matrices, respectively) and their products [A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, 1994; M.S. Gowda, Y. Song, Math. Prog. 88 (2000) 575–587; M.S. Gowda, T. Parthasarathy, Linear Algebra Appl. 320 (2...

Abstract A transformed primal-dual (TPD) flow is developed for a class of nonlinear smooth saddle point system. The the dual variable contains Schur complement which strongly convex. Exponential stability obtained by showing strong Lyapunov property. Several TPD iterations are derived implicit Euler, explicit implicit-explicit and Gauss-Seidel methods with accelerated overrelaxation flow. Gener...

A Banach space is polynomially Schur if sequential convergence against analytic polynomials implies norm convergence. Carne, Cole and Gamelin show that a space has this property and the Dunford-Pettis property if and only if it is Schur. Herein is defined a reasonable generalization of the Dunford–Pettis property using polynomials of a fixed homogeneity. It is shown, for example, that a Banach ...

In this article we introduce the flow polynomial of a digraph and use it to study nowherezero flows from a commutative algebraic perspective. Using Hilbert’s Nullstellensatz, we establish a relation between nowhere-zero flows and dual flows. For planar graphs this gives a relation between nowhere-zero flows and flows of their planar duals. It also yields an appealing proof that every bridgeless...

Abstract We define operator-valued Schur and Herz–Schur multipliers in terms of module actions, show that the standard properties these follow from well-known facts about actions duality theory for group actions. These results are applied to study an abelian acting on its Pontryagin dual: it is shown a natural subset can be identified with classical direct product dual group.