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Haglund–Haiman–Loehr formula criterion for Kostka–Macdonald polynomials
HaglundHaimanLoehr formula criterion. The formula is valid if and only if at least one of the following conditions holds: (i) $mu_1\leq 3$ and $mu_2\leq 2$ ; or (ii) $lambda$ is a h…
Conjectureopenalgebraic-combinatorics kostka-macdonald-polynomials symmetric-functionsarXiv posted 2 days ago
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Characterization of the explicit path formula for Kostka–Macdonald polynomials
Path-formula conjecture. The displayed explicit formula for the Kostka–Macdonald polynomial is valid if and only if at least one of the following conditions holds: (i)…
Conjectureopenkostka-macdonald-polynomials symmetric-functionsarXiv posted 2 days ago
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Independence of the generalized tau statistics
The generalized tau statistics are defined on paths in tensor products of rectangular Kirillov–Reshetikhin crystals by … where $u^{(r)}_s\in B^{r,s}$ is the highest element. Indepe…
Conjectureopencrystal-bases kostka-macdonald-polynomialsarXiv posted 2 days ago

Haglund–Haiman–Loehr formula criterion for Kostka–Macdonald polynomials