Geodesic
A link between the generating function of skew domino tableaux and quasisymmetric functions of type B
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 2, pp. 185-208 
A. R. Mayorova. A link between the generating function of skew domino tableaux and quasisymmetric functions of type B. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 2, pp. 185-208. http://geodesic.mathdoc.fr/item/FPM_2020_23_2_a9/
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     author = {A. R. Mayorova},
     title = {A~link between the generating function of skew domino tableaux and quasisymmetric functions of {type~B}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2020_23_2_a9/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider the generating function of skew domino tableaux and conditions of decomposing it using fundamental quasisymmetric functions of type B. This question, as showed earlier by Mayorova and Vassilieva, is related to the descent statistics for elements of Coxeter groups and tableaux for Coxeter groups. In this paper, we obtain estimates of the number of diagrams that fit the conditions.

[1] Adin R. M., Athanasiadis C. A., Elizalde S., Roichman Y., Character formulas and descents for the hyperoctahedral group, 2015, arXiv: 1504.01283 | MR

[2] Carré C., Leclerc B., “Splitting the square of a Schur function into its symmetric and antisymmetric parts”, J. Algebraic Combin., 4 (1995), 201–231 | DOI | MR | Zbl

[3] Chow C. O., Non Commutative Symmetric Functions of Type B, PhD thesis, MIT, 2001 | MR

[4] Elizalde S., Roichman Y., “Arc permutations”, J. Algebraic Combin., 39 (2014), 301–334 | DOI | MR | Zbl

[5] Gessel I., “Multipartite P-partitions and inner products of skew Schur functions”, Contemp. Math., 34 (1984), 289–317 | DOI | MR

[6] Mayorova A. R., Vassilieva E. A., “A domino tableau-based view on type B Schur-positivity”, Proc. of the 16th Int. Permutation Patterns Conf., 2018, 174–181

[7] Mayorova A. R., Vassilieva E. A., “A new link between the descent algebra of type B, domino tableaux and Chow's quasisymmetric functions”, Discrete Math., 342:6 (2019), 1658–1673 | DOI | MR | Zbl

[8] Solomon L., “A Mackey formula in the group ring of a Coxeter group”, J. Algebra, 41 (1976), 255–264 | DOI | MR

[9] Stanton D. W., White D. E., “A Schensted algorithm for rim hook tableaux”, J. Combin. Theory Ser. A, 40:2 (1985), 211–247 | DOI | MR | Zbl