The number of ribbon Schur functions.
The operation and operation of Cohen-Macaulay bipartite graphs
Let be a finite simple graph with the vertex set and let be its edge ideal in the polynomial ring . We compute the depth and the Castelnuovo-Mumford regularity of when or is a graph obtained from Cohen-Macaulay bipartite graphs , by the operation or operation, respectively.
The permutation classes equinumerous to the smooth class.
The plethysm at hook and near-hook shapes.
The product of trees in the Loday-Ronco algebra through Catalan alternative tableaux.
The ring of multisymmetric functions
We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring , thereby answering a classical question coming from works of F. Junker [J1, J2, J3] in the late nineteen century and then implicitly in H. Weyl book “The classical groups” [W].
The Robinson-Schensted correspondence, crystal bases, and the quantum straightening at .
The size of Fulton's essential set.
The skeleton of a reduced word and a correspondence of Edelman and Green.
The skew and relative derangements of type B.
The spectral excess theorem for distance-regular graphs: a global (over)view.
The Stanley-Féray-Śniady formula for the generalized characters of the symmetric group
We show that the explicit formula of Stanley-Féray-Śniady for the characters of the symmetric group has a natural extension to the generalized characters. These are the spherical functions of the unbalanced Gel’fand pair .
The strong persistence property and symbolic strong persistence property
Let be an ideal in a commutative Noetherian ring . Then the ideal has the strong persistence property if and only if for all , and has the symbolic strong persistence property if and only if for all , where denotes the th symbolic power of . We study the strong persistence property for some classes of monomial ideals. In particular, we present a family of primary monomial ideals failing the strong persistence property. Finally, we show that every square-free monomial ideal has the...
The strongly regular (40, 12, 2, 4) graphs.
The strongly regular (45, 12, 3, 3) graphs.
The use of Schubert polynomials in SYMCHAR.
The weighted hook length formula. III: Shifted tableaux.
The Young diagrams of a pair of irreducible characters of with the same zero set on .
Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture.
Thom polynomials and Schur functions: the singularities
We give the Thom polynomials for the singularities associated with maps with parameter . Our computations combine the characterization of Thom polynomials via the “method of restriction equations” of Rimanyi et al. with the techniques of Schur functions.