Computation of the $a$-invariant of ladder determinantal rings
Sudhir R. Ghorpade (IIT Bombay), Christian Krattenthaler, (Universit\"at Wien)
TL;DR
This paper presents methods to compute the $a$-invariant of ladder determinantal rings, offering a compact formula for one-sided ladders and an algorithmic approach for certain two-sided ladders.
Contribution
It introduces a compact formula for one-sided ladders and an algorithmic solution for a broad class of two-sided ladders, advancing the computation of the $a$-invariant.
Findings
Compact formula for one-sided ladders
Algorithmic solution for two-sided ladders
Effective computation of the $a$-invariant
Abstract
We solve the problem of effectively computing the -invariant of ladder determinantal rings. In the case of a one-sided ladder, we provide a compact formula, while, for a large family of two-sided ladders, we provide an algorithmic solution.
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