Results 11 to 20 of about 11,601,753 (180)
A generalization of the Murnaghan-Nakayama rule for $K$-$k$-Schur and $k$-Schur functions [PDF]
International Mathematics Research Notices, 2023 The $K$-$k$-Schur functions and $k$-Schur functions appeared in the study of $K$-theoretic and affine Schubert Calculus as polynomial representatives of Schubert classes.
Duc, Khanh Nguyen
core +4 more sources
A recursion formula for k-Schur functions [PDF]
Journal of Combinatorial Theory, Series A, 2009 The Bernstein operators allow one to build recursively the Schur functions. We present a recursion formula for k-Schur functions at t=1 based on combinatorial operators that generalize the Bernstein operators.
Lapointe, Luc, Bravo, Daniel
core +5 more sources
The down operator and expansions of near rectangular k-Schur functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We prove that the Lam-Shimozono ``down operator'' on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra of the affine nilCoxeter algebra. We use this to verify a conjecture of Berg, Bergeron, Pon and Zabrocki describing the
Chris Berg, Franco Saliola, Luis Serrano
doaj +10 more sources
A k-tableau characterization of k-Schur functions [PDF]
Advances in Mathematics, 2007 Luc Lapointe. Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile.We study k-Schur functions characterized by k-tableaux, proving combinatorial properties such as a k-Pieri rule and a k-conjugation.
Lapointe, L. +3 more
core +3 more sources
Closed $k$-Schur Katalan functions as $K$-homology Schubert representatives of the affine Grassmannian [PDF]
Transactions of the American Mathematical Society, Series B, 2023 Recently, Blasiak-Morse-Seelinger introduced symmetric functions called Katalan functions, and proved that the $K$-theoretic $k$-Schur functions due to Lam-Schilling-Shimozono form a subfamily of the Katalan functions.
Iwao, Shinsuke +2 more
core +4 more sources
A relationship between rational and multi-soliton solutions of the BKP hierarchy [PDF]
, 2005 We consider a special class of solutions of the BKP hierarchy which we call $\tau$-functions of hypergeometric type. These are series in Schur $Q$-functions over partitions, with coefficients parameterised by a function of one variable $\xi$, where the ...
Orlov, A.Y., Nimmo, J.J.C.
core +9 more sources
k-Schur expansions of Catalan functions [PDF]
Advances in Mathematics, 2020 33 ...
Blasiak, Jonah +3 more
+11 more sources
Expanding K-theoretic Schur Q-functions [PDF]
, 2023 We derive several identities involving Ikeda and Naruse’s K-theoretic Schur P- and Q-functions. Our main result is a formula conjectured by Lewis and the second author which expands each K-theoretic Schur Q-function in terms of K-theoretic Schur P ...
Yu-Cheng, Chiu, Marberg, Eric
core +2 more sources
Schubert Polynomials and $k$-Schur Functions [PDF]
The Electronic Journal of Combinatorics, 2014 The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type $A$ by a Schur function, which we refer to as Schubert vs. Schur problem, can be understood combinatorially from the multiplication in the space of dual $k$-Schur functions.
Carolina Benedetti, Nantel Bergeron
openaire +4 more sources
Notes on the Schur-convexity of the Extended Mean Values [PDF]
, 2002 In this article, the Schur-convexities of the weighted arithmetic mean of function and the extended mean values are proved. Moreover, some inequalities involving the arithmetic mean, the harmonic mean, the logarithmic mean, and comparison between the ...
Qi, Feng +3 more
core +6 more sources