Results 51 to 60 of about 159,494 (239)

Enumerative combinatorics on determinants and signed bigrassmannian polynomials

, 2019
As an application of linear algebra for enumerative combinatorics, we introduce two new ideas, signed bigrassmannian polynomials and bigrassmannian determinant. First, a signed bigrassmannian polynomial is a variant of the statistic given by the number of bigrassmannian permutations below a permutation in Bruhat order as Reading suggested (2002) and ...
Masato Kobayashi
openalex   +5 more sources

Asymmetric function theory

, 2019
The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry.
Allen Hatcher, Anders Skovsted Buch, Andrew Baker, B Yasmine, Bogdan Ion, C Lenart, Daniel Bump, David Anderson, E Dudley, Eric Opdam, Hugh Thomas, J Haglund, J Haglund, Masaki Kashiwara, Masaki Kashiwara, Masaki Kashiwara, Masaki Watanabe, Masaki Watanabe, Michiel Hazewinkel, N Ganter, Nantel Bergeron, Oliver Pechenik, Paul Bressler, Pavel Galashin, PN Norton, Rudolf Winkel, S Assaf, S Assaf, S Mason, Sara C Billey, Sergey Fomin, Thomas Hudson, V Reiner, Vasu V Tewari, W George, William Fulton, Witold Kraśkiewicz   +36 more
core   +1 more source

Unimodality Problems in Ehrhart Theory

, 2017
Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart $h^*$-vector. Ehrhart $h^*
A. Stapledon, Adam McCabe, Akihiro Higashitani, Alexander Postnikov, C. Bey, C. Haase, Carla D. Savage, Carla D. Savage, Christos A. Athanasiadis, E. Ehrhart, E. Katz, Federico Ardila, Francesco Brenti, H. Ohsugi, Hidefumi Ohsugi, I.M. Gelfand, Jan Schepers, Jeffrey C. Lagarias, Jesús A. De Loera, Jesús A. De Loera, Joseph Gubeladze, M. Beck, M. Hochster, M. Kreuzer, M. Mustaţǎ, Maria Chudnovsky, Matthias Beck, Matthias Beck, Matthias Beck, Matthias Beck, Mireille Bousquet-Mélou, Mordechai Katzman, Neil L. White, P. McMullen, R.P. Stanley, RICHARD P. STANLEY, Richard P. Stanley, S. Payne, T. Hibi, T. Hibi, Tadahito Harima, Takayuki Hibi, Takayuki Hibi, Thomas Lam, V.V. Batyrev, Winfried Bruns   +45 more
core   +1 more source

Rational Combinatorics [PDF]

, 2007
We propose a categorical setting for the study of the combinatorics of rational numbers. We find combinatorial interpretation for the Bernoulli and Euler numbers and polynomials.Comment: Adv. in Appl. Math.
Baez, Baez, Bergeron, Blandín, Díaz, Hassen, Héctor Blandín, Joyal, Joyal, Laplaza, Laplaza, Mac Lane, Rafael Díaz   +12 more
core   +8 more sources

Enumeration and Construction of Row‐Column Designs

Journal of Combinatorial Designs, EarlyView.
ABSTRACT We computationally completely enumerate a number of types of row‐column designs up to isotopism, including double, sesqui, and triple arrays as known from the literature, and two newly introduced types that we call mono arrays and AO‐arrays. We calculate autotopism group sizes for the designs we generate.
Gerold Jäger, Klas Markström, Denys Shcherbak, Lars‐Daniel Öhman   +3 more
wiley   +1 more source

Enumeration of E(s2) $\,E({s}^{2})$‐Optimal and Minimax‐Optimal Supersaturated Designs With 12 Rows, 11q $11q$ Columns and smax=4 ${s}_{{\rm{\max }}}=4$

Journal of Combinatorial Designs, EarlyView.
ABSTRACT The E(s2) $\,E({s}^{2})$‐optimal and minimax‐optimal supersaturated designs (SSDs) with 12 rows, 11q $11q$ columns, and smax=4 ${s}_{{\rm{\max }}}=4$ are enumerated in a computer search: there are, respectively, 34, 146, 0, 3, and 1 such designs for q=2,3,4,5 $q=2,3,4,5$, and 6.
Luis B. Morales
wiley   +1 more source

Symmetric 2‐( 35 , 17 , 8 ) $(35,17,8)$ Designs With an Automorphism of Order 2

Journal of Combinatorial Designs, EarlyView.
ABSTRACT The largest prime p $p$ that can be the order of an automorphism of a 2‐( 35 , 17 , 8 ) $(35,17,8)$ design is p = 17 $p=17$, and all 2‐( 35 , 17 , 8 ) $(35,17,8)$ designs with an automorphism of order 17 were classified by Tonchev. The symmetric 2‐( 35 , 17 , 8 ) $(35,17,8)$ designs with automorphisms of an odd prime order p < 17 $p\lt 17 ...
Sanja Rukavina, Vladimir D. Tonchev
wiley   +1 more source

New directions in enumerative chess problems [PDF]

, 2005
Normally a chess problem must have a unique solution, and is deemed unsound even if there are alternatives that differ only in the order in which the same moves are played.
Elkies, Noam D.
core   +1 more source

Extremal, enumerative and probabilistic results on ordered hypergraph matchings

Forum of Mathematics, Sigma
An ordered r-matching is an r-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of r-dimensional orders.
Michael Anastos, Zhihan Jin, Matthew Kwan, Benny Sudakov   +3 more
doaj   +1 more source

Abundant Neighborhoods, Two‐Sided Markets, and Maximal Matchings

Naval Research Logistics (NRL), EarlyView.
ABSTRACT I introduce a new graph‐theoretic property called abundant neighborhoods. This property is motivated by studying the thickness of economic markets. A vertex is, roughly, guaranteed to match if and only if it has an abundant neighborhood.
Muhammad Maaz
wiley   +1 more source