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13 papers · 1 filter
Erdős-Szekeres theorem for -flats
Imre Bárány, Gil Kalai, Attila Pór
We extend the famous Erdős-Szekeres theorem to -flats in
Sign-alternating Gibonacci polynomials
Robert G. Donnelly, Molly W. Dunkum, Murray L. Huber +1
We consider various properties and manifestations of some sign-alternating univariate polynomials borne of right-triangular integer arrays related to certain generalizations of the…
Symmetric Fibonaccian distributive lattices and representations of the special linear Lie algebras
Robert G. Donnelly, Molly W. Dunkum, Sasha V. Malone +1
We present a family of rank symmetric diamond-colored distributive lattices that are naturally related to the Fibonacci sequence and certain of its generalizations. These lattices…
Random bipartite posets and extremal problems
Csaba Biró, Peter Hamburger, H. A. Kierstead +3
Previously, Erdős, Kierstead and Trotter investigated the dimension of random height~ partially ordered sets. Their research was motivated primarily by two goals: (1)~analyzing…
Move-minimizing puzzles and diamond-colored modular/distributive lattices
Robert G. Donnelly, Elizabeth A. Donovan, Molly W. Dunkum +1
The move-minimizing puzzles presented here are certain types of one-player combinatorial games that are shown to have explicit solutions whenever they can be encoded in a certain w…
Forcing Posets with Large Dimension to Contain Large Standard Examples
Csaba Biró, Peter Hamburger, Attila Pór +1
The dimension of a poset , denoted , is the least positive integer for which is the intersection of linear extensions of . The maximum dimension of a pos…