On flagged KK-theoretic symmetric polynomials

We provide a fermionic description of flagged skew Grothendieck polynomials, which can be seen as a $K$-theoretic counterpart of flagged skew Schur polynomials. Our proof relies on the Jacobi-Trudi type formula established by Matsumura. This result generalizes the author's previous works on a fermionic description of skew Grothendieck polynomials and multi-Schur functions.Comment: 8page

Hook formulas for skew shapes

International audienceThe celebrated hook-length formula gives a product formula for the number of standard Young tableaux of a straight shape. In 2014, Naruse announced a more general formula for the number of standard Young tableaux of skew shapes as a positive sum over excited diagrams of products of hook-lengths. We give two q-analogues of Naruse's formula for the skew Schur functions and for counting reverse plane partitions of skew shapes. We also apply our results to border strip shapes and their generalizations

Hook formulas for skew shapes

The celebrated hook-length formula gives a product formula for the number of standard Young tableaux of a straight shape. In 2014, Naruse announced a more general formula for the number of standard Young tableaux of skew shapes as a positive sum over excited diagrams of products of hook-lengths. We give two q-analogues of Naruse's formula for the skew Schur functions and for counting reverse plane partitions of skew shapes. We also apply our results to border strip shapes and their generalizations