Related papers: A New Partial Order on SYT
A tableau inversion is a pair of entries from the same column of a row-standard tableau that lack the relative ordering necessary to make the tableau column-standard. An $i$-inverted Young tableau is a row-standard tableau with precisely…
Partially ordered sets of type (k, n) are the sets such that a) cardinality of each set is n, b) dimension of each set is two, c) length of the maximal antichain in each set is k. Let \alpha_k(n) be the number of partially ordered sets of…
We give the first data structure for the problem of maintaining a dynamic set of n elements drawn from a partially ordered universe described by a tree. We define the Line-Leaf Tree, a linear-sized data structure that supports the…
The number of standard Young tableaux of a fixed shape is famously given by the hook-length formula due to Frame, Robinson and Thrall. A bijective proof of Novelli, Pak and Stoyanovskii relies on a sorting algorithm akin to jeu-de-taquin…
Starting with real line number system based on the theory of the Yang's fractional set, the generalized Young inequality is established. By using it some results on the generalized inequality in fractal space are investigated in detail.
We examine a few families of semistandard Young tableaux, for which we observe the cyclic sieving phenomenon under promotion. The first family we consider consists of stretched hook shapes, where we use the cocharge generating polynomial as…
We propose a novel in-order chart-based model for constituent parsing. Compared with previous CKY-style and top-down models, our model gains advantages from in-order traversal of a tree (rich features, lookahead information and high…
A number of recent papers treated the representation theory of partially ordered sets in unitary spaces with the so called orthoscalar relation. Such theory generalizes the classical theory which studies the representations of partially…
We propose a new class of mathematical structures called (m,n)-semirings} (which generalize the usual semirings), and describe their basic properties. We also define partial ordering, and generalize the concepts of congruence, homomorphism,…
The first steps towards linearisation of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that…
We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given.
This paper introduces the seed order, a partial order of the class of uniform countably complete ultrafilters that generalizes the Mitchell order on normal measures. Like that order, the seed order is consistently a linear ordering even…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
The notion of a barely set-valued semistandard Young tableau was introduced by Reiner, Tenner and Yong in their study of the probability distribution of edges in the Young lattice of partitions. Given a partition $\lambda$ and a positive…
The present work is dedicated to searching parameters, alternative to entropy, applicable for description of highly organized systems. The general concept has been offered, in which the system complexity and order are functions of the order…
We give a more coherent definition of upward planar order.
As a motivation, we first recall the possible connection of electric-magnetic duality to finiteness in N=1 super-Yang-Mills theories (SYM). Then, we present the criterion for all-order finiteness (i.e., vanishing of the beta-functions at…
Let $\mathcal{CT}_n$ be the semigroup of full contraction mappings on $[n]=\{1,2,\ldots,n\}$, and let $\mathcal{OCT}_n$ and $\mathcal{ODCT}_n$ be the subsemigroups consisting of all order-preserving full contraction and subsemigroup of…
This paper is concerned with structures of general graphs with perfect matchings. We first reveal a partially ordered structure among factor-components of general graphs with perfect matchings. Our second result is a generalization of…
In the present paper we introduce a lattice-ordered partial monoid structure on a suitable set of multilayer networks. We first study a kind of mappings that preserve the partial order and describe the order structure. After that we define…