Vertically symmetric alternating sign matrices and a multivariate Laurent polynomial identity

In 2007, the first author gave an alternative proof of the refined alternating sign matrix theorem by introducing a linear equation system that determines the refined ASM numbers uniquely. Computer experiments suggest that the numbers appearing in a conjecture concerning the number of vertically symmetric alternating sign matrices with respect to the position of the first 1 in the second row of the matrix establish the solution of a linear equation system similar to the one for the ordinary refined ASM numbers. In this paper we show how our attempt to prove this fact naturally leads to a more general conjectural multivariate Laurent polynomial identity. Remarkably, in contrast to the ordinary refined ASM numbers, we need to extend the combinatorial interpretation of the numbers to parameters which are not contained in the combinatorial admissible domain. Some partial results towards proving the conjectured multivariate Laurent polynomial identity and additional motivation why to study it are presented as well

Metamodelling a formal method : applying MDE to abstract state machines

This paper presents the AsmM, a metamodel for Abstract State Machines developed by following the guidelines of the Model Driven Engineering. The AsmM represents concepts and constructs of the ASM formal method in an abstract way, it is endowed with a standard visual notation, and it is intended easy to learn and understand by practitioners and students. From the AsmM a concrete syntax is also proposed and a standard interchange format for a systematic integration of a number of loosely-coupled ASM tools is derived. The metamodelling advantages for tool interoperability are shown by referring to the experience in making the ATGT, an existing tool supporting test case generation for ASMs, compliant to the AsmM

LEMP : a language engineering model-driven process

In this paper, we propose LEMP as a model-driven process to develop a language endowed with a set of derived artifacts (syntax, interchange format, APIs, ...) and with a well defined formal semantics. The process exploits the Model Driven Engineering principles of metamodeling, model transformation and automatic generation of language processing tools. We describe the requirements to fulfill and the development steps of this language engineering life cycle, including the validation activities regarding the syntactic and semantic aspects. As a proof-of-concepts, we apply LEMP to the Finite State Machines and we report our experience in developing a language for the Abstract State Machine formal method

Refined Cauchy/Littlewood identities and six-vertex model partition functions: II. Proofs and new conjectures

We prove two identities of Hall-Littlewood polynomials, which appeared recently in a paper by two of the authors. We also conjecture, and in some cases prove, new identities which relate infinite sums of symmetric polynomials and partition functions associated with symmetry classes of alternating sign matrices. These identities generalize those already found in our earlier paper, via the introduction of additional parameters. The left hand side of each of our identities is a simple refinement of a relevant Cauchy or Littlewood identity. The right hand side of each identity is (one of the two factors present in) the partition function of the six-vertex model on a relevant domain.Comment: 34 pages, 14 figure