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1. Potentially Hurwitz Structures: A Characterization of Nests

   https://doi.org/10.1109/CDC42340.2020.9304453  

   Cavalcanti, Joao (December 2020, 2020 59th IEEE Conference on Decision and Control (CDC))
2. Dens, nests and the Loehr-Warrington conjecture

   https://doi.org/10.1090/jams/1057  

   Blasiak, J; Haiman, M; Morse, J; Pun, A; Seelinger, G (June 2025, Journal of the American Mathematical Society)

   We prove and extend the longest-standing conjecture in ‘ $q,t$-Catalan combinatorics,’ namely, the combinatorial formula for ${\mathrm{\nabla <\#comment/>}}^m{s}_{\mathrm{\mu <\#comment/>}}$conjectured by Loehr and Warrington, where $s_{\mathrm{\mu <\#comment/>}}$is a Schur function and $\mathrm{\nabla <\#comment/>}$is an eigenoperator on Macdonald polynomials. Our approach is to establish a stronger identity of infinite series of $G{L}_l$characters involvingSchur Catalanimals; these were recently shown by the authors to represent Schur functions $s_{\mathrm{\mu <\#comment/>}}[-<\#comment/>M{X}^{m,n}]$in subalgebras $\mathrm{\Lambda <\#comment/>}\left(X^{m,n}\right)\subset <\#comment/>\mathcal{E}$isomorphic to the algebra of symmetric functions $\mathrm{\Lambda <\#comment/>}$over $\mathbb{Q}(q,t)$, where $\mathcal{E}$is the elliptic Hall algebra of Burban and Schiffmann. We establish a combinatorial formula for Schur Catalanimals as weighted sums of LLT polynomials, with terms indexed by configurations of nested lattice paths callednests, having endpoints and bounding constraints controlled by data called aden. The special case for $\mathrm{\Lambda <\#comment/>}\left(X^{m,1}\right)$proves the Loehr-Warrington conjecture, giving ${\mathrm{\nabla <\#comment/>}}^m{s}_{\mathrm{\mu <\#comment/>}}$as a weighted sum of LLT polynomials indexed by systems of nested Dyck paths. In general, for $\mathrm{\Lambda <\#comment/>}\left(X^{m,n}\right)$our formula implies a new $(m,n)$version of the Loehr-Warrington conjecture. In the case where each nest consists of a single lattice path, the nests in a den formula reduce to our previous shuffle theorem for paths under any line. Both this and the $(m,n)$Loehr-Warrington formula generalize the $(km,kn)$shuffle theorem proven by Carlsson and Mellit (for $n=1$) and Mellit. Our formula here unifies these two generalizations. 

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3. Worker task organization in incipient bumble bee nests

   https://doi.org/10.1016/j.anbehav.2021.12.005  

   Fisher, K; Sarro, E; Miranda, C; B Guillen, B; Woodard, SH. (January 2022, Animal behaviour)
4. Noisy nests: Early-life noise exposure impacts songbird fitness

   https://doi.org/10.3758/s13420-024-00654-z  

   Templeton, Christopher N (June 2025, Learning & Behavior)
5. Ant nests differentially affect soil chemistry across elevational gradients

   https://doi.org/10.1007/s00040-022-00869-1  

   Sankovitz, M.; Purcell, J. (July 2022, Insectes Sociaux)

   Abstract Ants alter soil moisture and nutrient distributions during foraging and nest construction. Here, we investigated how the effects of ants on soil vary with elevation. We compared moisture, carbon, and nitrogen levels in soil samples taken both within nests and nearby the nests (control) of two subterranean ant species. Using a paired design, we sampled 17 sites along elevation gradients in two California mountain ranges (Formica francoeuriin the San Jacinto mountains andFormica sibyllain the Sierra Nevada). We observed an interaction between soil carbon and nitrogen composition and elevation in each mountain range. At lower elevations, nest soil had lower amounts of carbon and nitrogen than control soil, but at higher elevations, nest soil had higher amounts of carbon and nitrogen than control soil. However, our sampling method may only breach the interior of ant nests in some environments. The nest soil moisture did not show any elevational patterns in either mountain range. Ants likely modulate soil properties differently across environmental gradients, but testing this effect must account for variable nest architecture and other climate and landscape differences across diverse habitats. 

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