Geodesic
On Faces and Hilbert Bases of Kostka Cones
The electronic journal of combinatorics, Tome 32 (2025) no. 4
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The $r$-Kostka cone is the real polyhedral cone generated by pairs of partitions with at most $r$ parts such that the corresponding Kostka coefficient is nonzero. We provide several results showing that its faces have interesting structural and enumerative properties. We show that, for fixed $d$, the number of $d$-faces of the $r$-Kostka cone is a polynomial in $r$ with a positive integer expansion in the binomial basis, and we provide exact formulas for $d \leq 4$. We prove that the maximum number of extremal rays in a $d$-face stabilizes to some explicit constant as $r$ increases. We then work towards a generalization of the Gao-Kiers-Orelowitz-Yong Width Bound.
DOI : 10.37236/13472

Amanda Burcroff  1

1 MIT 
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     author = {Amanda Burcroff},
     title = {On {Faces} and {Hilbert} {Bases} of {Kostka} {Cones}},
     journal = {The electronic journal of combinatorics},
     year = {2025},
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     number = {4},
     doi = {10.37236/13472},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/13472/}
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Amanda Burcroff. On Faces and Hilbert Bases of Kostka Cones. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/13472

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