Linear spaces, transversal polymatroids and ASL domains
Aldo Conca
Universitá di Genova Dipartimento di Matematica Genova Italy Genova Italy
DOI: 10.1007/s10801-006-0026-3
Abstract
We study a class of algebras associated with linear spaces and its relations with polymatroids and integral posets, i.e. posets supporting homogeneous ASL. We prove that the base ring of a transversal polymatroid is Koszul and describe a new class of integral posets. As a corollary we obtain that every Veronese subring of a polynomial ring is an ASL.
Pages: 25–41
Keywords: keywords families of linear spaces; transversal polymatroids; Koszul algebras; ASL; Veronese rings; Gröbner bases
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References
1. A. Aramova, K. Crona, and E. De Negri, “Bigeneric initial ideals, diagonal subalgebras and bigraded Hilbert functions,” J. Pure Appl. Algebra 150(3) (2000), 215-235.
2. W. Bruns and A. Conca, “Gr\ddot obner bases and determinantal ideals,” Commutative Algebra, Singularities and Computer Algebra (Sinaia, 2002), pp. 9-66, NATO Sci. Ser. II Math. Phys. Chem., 115, Kluwer Acad. Publ., Dordrecht, 2003.
3. W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge University Press, Cambridge, 1996.
4. W. Bruns and U. Vetter, Determinantal rings, Lecture Notes in Mathematics,
1327. Springer-Verlag, Berlin, 1988.
5. CoCoA Team, CoCoA: A System for doing Computations in Commutative Algebra, Available at
2. W. Bruns and A. Conca, “Gr\ddot obner bases and determinantal ideals,” Commutative Algebra, Singularities and Computer Algebra (Sinaia, 2002), pp. 9-66, NATO Sci. Ser. II Math. Phys. Chem., 115, Kluwer Acad. Publ., Dordrecht, 2003.
3. W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge University Press, Cambridge, 1996.
4. W. Bruns and U. Vetter, Determinantal rings, Lecture Notes in Mathematics,
1327. Springer-Verlag, Berlin, 1988.
5. CoCoA Team, CoCoA: A System for doing Computations in Commutative Algebra, Available at