The enumeration of diagonally symmetric alternating sign matrices (DSASMs) is studied, and a Pfaffian formula is obtained for the number of DSASMs of any fixed size, where the entries for the Pfaffian are positive integers given by simple binomial coefficient expressions. This result provides the first known case of an exact enumeration formula for an alternating sign matrix symmetry class in which a simple product formula does not seem to exist. Pfaffian formulae are also obtained for DSASM generating functions associated with several natural statistics, including the number of nonzero strictly upper triangular entries in a DSASM, the number of nonzero diagonal entries in a DSASM, and the column number of the unique 1 in the first row of a DSASM. The proofs of these results involve introducing a version of the six-vertex model whose configurations are in bijection with DSASMs of fixed size, and obtaining a Pfaffian expression for its partition function. Various related topics are also studied, involving diagonally symmetric permutation matrices, off-diagonally symmetric alternating sign matrices, certain natural involutions on DSASMs, and the asymptotic enumeration of DSASMs and other classes of alternating sign matrices. (c) 2026 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

Galaxies at redshift z similar to 2-6 exhibit prominent star-forming regions (clumps). Characterization of these galactic structures requires both high sensitivity and spatial resolution of similar to 100 pc or less. Currently, these spatial scales are achievable only with the aid of strong gravitational lensing. However, lensing introduces model-dependent uncertainties and limits the sample to galaxies behind massive clusters. The upcoming 40 m-class telescopes, such as the ESO Extremely Large Telescope (ELT), will enable routine studies of clumps in ubiquitous, non-lensed z >= 2 galaxies. We assess the capability of MICADO, the first-light imager and spectrograph of the ELT, to characterize clumps in non-lensed z = 2 galaxies. Specifically, we focus on two representative observing scenarios, providing the basis for an early scientific exploitation of the instrument. We modelled clumps in an idealized z = 2 star-forming galaxy and produced mock MICADO observations in both broad-and narrow-band imaging. The latter leverages the strong emission lines typical of clumps to improve detection and characterization. Reaching UVrest-frame magnitudes of clumps asfaint as M-UV similar to-15 in optimal observing conditions, MICADO will be able to efficiently characterize clumps in non-lensed z = 2 galaxies down to R-e similar to 20 pc. Moreover, the full MICADO similar to 1 arcmin(2) field of view enables efficientsurveys of multiple targets. Thisstudy demonstrates MICADO's potential to fill a crucial observational gap, shedding new light on clump formation and evolution at cosmic noon. Accurate PSF reconstruction will be crucial to fully harnessthis capability asitsignificantly impacts clump detection and characterization, especially at the smallest sizes (< 40 pc).