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In Section 13, we discuss flagged Schur polynomials, vexillary and dominant permutations, and give a simple formula for the polynomials D w , for 312-avoiding permutations.. In

Analogs of this theorem were proved by Roitberg for nonregular elliptic boundary- value problems and for general elliptic systems of differential equations, the mod- ified scale of

“Breuil-M´ezard conjecture and modularity lifting for potentially semistable deformations after

Then it follows immediately from a suitable version of “Hensel’s Lemma” [cf., e.g., the argument of [4], Lemma 2.1] that S may be obtained, as the notation suggests, as the m A

Correspondingly, the limiting sequence of metric spaces has a surpris- ingly simple description as a collection of random real trees (given below) in which certain pairs of

[Mag3] , Painlev´ e-type differential equations for the recurrence coefficients of semi- classical orthogonal polynomials, J. Zaslavsky , Asymptotic expansions of ratios of

The issue is that unlike for B ℵ 1 sets, the statement that a perfect set is contained in a given ω 1 -Borel set is not necessarily upwards absolute; if one real is added to a model

p≤x a 2 p log p/p k−1 which is proved in Section 4 using Shimura’s split of the Rankin–Selberg L -function into the ordinary Riemann zeta-function and the sym- metric square