Reduction of mm-Regular Noncrossing Partitions

In this paper, we present a reduction algorithm which transforms $m$-regular partitions of $[n]=\{1, 2, ..., n\}$ to $(m-1)$-regular partitions of $[n-1]$. We show that this algorithm preserves the noncrossing property. This yields a simple explanation of an identity due to Simion-Ullman and Klazar in connection with enumeration problems on noncrossing partitions and RNA secondary structures. For ordinary noncrossing partitions, the reduction algorithm leads to a representation of noncrossing partitions in terms of independent arcs and loops, as well as an identity of Simion and Ullman which expresses the Narayana numbers in terms of the Catalan numbers

Riordan Paths and Derangements

Riordan paths are Motzkin paths without horizontal steps on the x-axis. We establish a correspondence between Riordan paths and $(321,3\bar{1}42)$-avoiding derangements. We also present a combinatorial proof of a recurrence relation for the Riordan numbers in the spirit of the Foata-Zeilberger proof of a recurrence relation on the Schr\"oder numbers.Comment: 9 pages, 2 figure

Assessing effects of permafrost thaw on C fluxes based on multiyear modeling across a permafrost thaw gradient at Stordalen, Sweden

Northern peatlands in permafrost regions contain a large amount of organic carbon (C) in the soil. Climate warming and associated permafrost degradation are expected to have significant impacts on the C balance of these ecosystems, but the magnitude is uncertain. We incorporated a permafrost model, Northern Ecosystem Soil Temperature (NEST), into a biogeochemical model, DeNitrificationDeComposition (DNDC), to model C dynamics in highlatitude peatland ecosystems. The enhanced model was applied to assess effects of permafrost thaw on C fluxes of a subarctic peatland at Stordalen, Sweden. DNDC simulated soil freeze–thaw dynamics, net ecosystem exchange of CO2 (NEE), and CH4 fluxes across three typical land cover types, which represent a gradient in the process of ongoing permafrost thaw at Stordalen. Model results were compared with multiyear field measurements, and the validation indicates that DNDC was able to simulate observed differences in seasonal soil thaw, NEE, and CH4 fluxes across the three land cover types. Consistent with the results from field studies, the modeled C fluxes across the permafrost thaw gradient demonstrate that permafrost thaw and the associated changes in soil hydrology and vegetation not only increase net uptake of C from the atmosphere but also increase the annual to decadal radiative forcing impacts on climate due to increased CH4 emissions. This study indicates the potential of utilizing biogeochemical models, such as DNDC, to predict the soil thermal regime in permafrost areas and to investigate impacts of permafrost thaw on ecosystem C fluxes after incorporating a permafrost component into the model framework