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

Realizing arbitrarily large spectra of aT\mathfrak{a}_{\text{T}}

We improve the state-of-the-art proof techniques for realizing various spectra of $\mathfrak{a}_{\text{T}}$ in order to realize arbitrarily large spectra. Thus, we make significant progress in addressing a question posed by Brian in his recent work. As a by-product, we obtain many complete subforcings and an algebraic analysis of the automorphisms of the forcing which adds a witness for the spectrum of $\mathfrak{a}_{\text{T}}$ of desired size.Comment: 41 pages, submitte

Combinatorial Reciprocity for Monotone Triangles

The number of Monotone Triangles with bottom row k1 < k2 < ... < kn is given by a polynomial alpha(n; k1,...,kn) in n variables. The evaluation of this polynomial at weakly decreasing sequences k1 >= k2 >= ... >= kn turns out to be interpretable as signed enumeration of new combinatorial objects called Decreasing Monotone Triangles. There exist surprising connections between the two classes of objects -- in particular it is shown that alpha(n; 1,2,...,n) = alpha(2n; n,n,n-1,n-1,...,1,1). In perfect analogy to the correspondence between Monotone Triangles and Alternating Sign Matrices, the set of Decreasing Monotone Triangles with bottom row (n,n,n-1,n-1,...,1,1) is in one-to-one correspondence with a certain set of ASM-like matrices, which also play an important role in proving the claimed identity algebraically. Finding a bijective proof remains an open problem.Comment: 24 page

What's the Difference Between Professional Human and Machine Translation? A Blind Multi-language Study on Domain-specific MT

Machine translation (MT) has been shown to produce a number of errors that require human post-editing, but the extent to which professional human translation (HT) contains such errors has not yet been compared to MT. We compile pre-translated documents in which MT and HT are interleaved, and ask professional translators to flag errors and post-edit these documents in a blind evaluation. We find that the post-editing effort for MT segments is only higher in two out of three language pairs, and that the number of segments with wrong terminology, omissions, and typographical problems is similar in HT.Comment: EAMT 2020 (Research Track

Universally Sacks-indestructible combinatorial families of reals

We introduce the notion of an arithmetical type of combinatorial family of reals, which serves to generalize different types of families such as mad families, maximal cofinitary groups, ultrafilter bases, splitting families and other similar types of families commonly studied in combinatorial set theory. We then prove that every combinatorial family of reals of arithmetical type, which is indestructible by the product of Sacks forcing $\mathbb{S}^{\aleph_0}$, is in fact universally Sacks-indestructible, i.e. it is indestructible by any countably supported iteration or product of Sacks-forcing of any length. Further, under $\text{CH}$ we present a unified construction of universally Sacks-indestructible families for various arithmetical types of families. In particular we prove the existence of a universally Sacks-indestructible maximal cofinitary group under $\text{CH}$.Comment: 33 pages, submitte