Related papers: Product formulas for certain skew tableaux

When present, the Cohen-Macaulay property can be useful for finding the minimal defining equations of an algebraic variety. It is conjectured that all secant varieties of Segre products of projective spaces are arithmetically…

We give a combinatorial expansion of the stable Grothendieck polynomials of skew Young diagrams in terms of skew Schur functions, using a new row insertion algorithm for set-valued semistandard tableaux of skew shape. This expansion unifies…

MacMahon proved a simple product formula for the generating function of plane partitions fitting in a given box. The theorem implies a $q$-enumeration of lozenge tilings of a semi-regular hexagon on the triangular lattice. In this paper we…

In this paper, we take interest in finding applications for a hook-length formula recently proved in (Morales Pak Panova 2016). This formula can be applied to give a non trivial relation between alternating permutations and weighted Dyck…

We show that sequences of skew Schur polynomials obtained from stretched semi-standard Young tableaux satisfy a linear recurrence, which we give explicitly. Using this, we apply this to finding certain asymptotic behavior of these Schur…

Let SYT_n be the set of all standard Young tableaux with n cells. After recalling the definitions of four partial orders, the weak, KL, geometric and chain orders on SYT_n and some of their crucial properties, we prove three main results:…

Intrigued by the product formula prod_{i=1}^{n-2} C_i for the volume of the Chan-Robbins-Yuen polytope CRY_n, where C_i is the ith Catalan number, we construct a family of polytopes P_{m,n}, whose volumes are given by the product…

We give a counting formula for the set of rectangular increasing tableaux in terms of generalized Narayana numbers. We define small $m$-Schr\"oder paths and give a bijection between the set of increasing rectangular tableaux and small…

Let $\phi: M\to M$ be a diffeomorphism of a $C^\infty$ compact connected manifold, and $X$ its mapping torus. There is a natural fibration $p:X\to S^1$, denote by $\xi\in H^1(X, \mathbb{Z})$ the corresponding cohomology class. Let…

The Hopf sign conjecture states that a compact Riemannian 2d-manifold M of positive curvature has Euler characteristic X(M)>0 and that in the case of negative curvature X(M) (-1)^d >0. The Hopf product conjecture asks whether a positive…

Let $H_n(t)$ denote the classical Rogers-Szeg\"o polynomial, and let $\tH_n(t_1, \ldots, t_l)$ denote the homogeneous Rogers-Szeg\"o polynomial in $l$ variables, with indeterminate $q$. There is a classical product formula for…

In this paper we study certain variational aspects of the volume product functional restricted to the space of small projective deformations of a fixed convex body. In doing so, we provide a short proof of a theorem by Klartag: a strong…

In earlier work with C.~Monical, we introduced the notion of a K-crystal, with applications to K-theoretic Schubert calculus and the study of Lascoux polynomials. We conjectured that such a K-crystal structure existed on the set of…

In recent work, Griffin, Ono, and Tsai constructs an $L-$series to prove that the proportion of short Weierstrass elliptic curves over $\mathbb{Q}$ with trivial Tamagawa product is $0.5054\dots$ and that the average Tamagawa product is…

There are representations of the type-A Hecke algebra on spaces of polynomials in anti-commuting variables. Luque and the author [S\'em. Lothar. Combin. 66 (2012), Art. B66b, 68 pages, arXiv:1106.0875] constructed nonsymmetric Macdonald…

We study stable commutator length (scl) in free products via surface maps into a wedge of spaces. We prove that scl is piecewise rational linear if it vanishes on each factor of the free product, generalizing the main result in Danny…

Given two vectors $u$ and $v$, their outer sum is given by the matrix $A$ with entries $A_{ij} = u_{i} + v_{j}$. If the entries of $u$ and $v$ are increasing and sufficiently generic, the total ordering of the entries of the matrix is a…

A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on representation theory of Brauer algebras. A general procedure for the decomposition of tensor products of representations for O(n) and…

A randomisation of the Berele insertion algorithm is proposed, where the insertion of a letter to a symplectic Young tableau leads to a distribution over the set of symplectic Young tableaux. Berele's algorithm provides a bijection between…

Assuming Stanley's $P$-partition conjecture holds, the regular Schur labeled skew shape posets with underlying set $\{1,2,\ldots, n\}$ are precisely the posets $P$ such that the $P$-partition generating function is symmetric and the set of…