Picture of a black hole

Strathclyde Open Access research that creates ripples...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of research papers by University of Strathclyde researchers, including by Strathclyde physicists involved in observing gravitational waves and black hole mergers as part of the Laser Interferometer Gravitational-Wave Observatory (LIGO) - but also other internationally significant research from the Department of Physics. Discover why Strathclyde's physics research is making ripples...

Strathprints also exposes world leading research from the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

Enumerating (2+2) -free posets by the number of minimal elements and other statistics

Kitaev, Sergey and Remmel, Jeffrey (2011) Enumerating (2+2) -free posets by the number of minimal elements and other statistics. Discrete Mathematics, 159 (17). 2098 - 2108.

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

An unlabeled poset is said to be -free if it does not contain an induced subposet that is isomorphic to , the union of two disjoint 2-element chains. Let pn denote the number of -free posets of size n. In a recent paper, Bousquet-Mélou et al. [1] found, using the so called ascent sequences, the generating function for the number of -free posets of size n: . We extend this result in two ways. First, we find the generating function for -free posets when four statistics are taken into account, one of which is the number of minimal elements in a poset. Second, we show that if pn,k equals the number of -free posets of size n with k minimal elements, then . The second result cannot be derived from the first one by a substitution. Our enumeration results are extended to certain restricted permutations and to regular linearized chord diagrams through bijections in [1] and [2]. Finally, we define a subset of ascent sequences counted by the Catalan numbers and we discuss its relations with - and -free posets. An unlabeled poset is said to be -free if it does not contain an induced subposet that is isomorphic to , the union of two disjoint 2-element chains. Let pn denote the number of -free posets of size n. In a recent paper, Bousquet-Mélou et al. [1] found, using the so called ascent sequences, the generating function for the number of -free posets of size n: . We extend this result in two ways. First, we find the generating function for -free posets when four statistics are taken into account, one of which is the number of minimal elements in a poset. Second, we show that if pn,k equals the number of -free posets of size n with k minimal elements, then . The second result cannot be derived from the first one by a substitution. Our enumeration results are extended to certain restricted permutations and to regular linearized chord diagrams through bijections in [1] and [2]. Finally, we define a subset of ascent sequences counted by the Catalan numbers and we discuss its relations with - and -free posets. An unlabeled poset is said to be -free if it does not contain an induced subposet that is isomorphic to , the union of two disjoint 2-element chains. Let pn denote the number of -free posets of size n. In a recent paper, Bousquet-Mélou et al. [1] found, using the so called ascent sequences, the generating function for the number of -free posets of size n: . We extend this result in two ways. First, we find the generating function for -free posets when four statistics are taken into account, one of which is the number of minimal elements in a poset. Second, we show that if pn,k equals the number of -free posets of size n with k minimal elements, then . The second result cannot be derived from the first one by a substitution. Our enumeration results are extended to certain restricted permutations and to regular linearized chord diagrams through bijections in [1] and [2]. Finally, we define a subset of ascent sequences counted by the Catalan numbers and we discuss its relations with - and -free posets. An unlabeled poset is said to be -free if it does not contain an induced subposet that is isomorphic to , the union of two disjoint 2-element chains. Let pn denote the number of -free posets of size n. In a recent paper, Bousquet-Mélou et al. [1] found, using the so called ascent sequences, the generating function for the number of -free posets of size n: . We extend this result in two ways. First, we find the generating function for -free posets when four statistics are taken into account, one of which is the number of minimal elements in a poset. Second, we show that if pn,k equals the number of -free posets of size n with k minimal elements, then . The second result cannot be derived from the first one by a substitution. Our enumeration results are extended to certain restricted permutations and to regular linearized chord diagrams through bijections in [1] and [2]. Finally, we define a subset of ascent sequences counted by the Catalan numbers and we discuss its relations with - and -free posets. An unlabeled poset is said to be -free if it does not contain an induced subposet that is isomorphic to , the union of two disjoint 2-element chains. Let pn denote the number of -free posets of size n. In a recent paper, Bousquet-Mélou et al. [1] found, using the so called ascent sequences, the generating function for the number of -free posets of size n: . We extend this result in two ways. First, we find the generating function for -free posets when four statistics are taken into account, one of which is the number of minimal elements in a poset. Second, we show that if pn,k equals the number of -free posets of size n with k minimal elements, then . The second result cannot be derived from the first one by a substitution. Our enumeration results are extended to certain restricted permutations and to regular linearized chord diagrams through bijections in [1] and [2]. Finally, we define a subset of ascent sequences counted by the Catalan numbers and we discuss its relations with - and -free posets. An unlabeled poset is said to be -free if it does not contain an induced subposet that is isomorphic to , the union of two disjoint 2-element chains. Let pn denote the number of -free posets of size n. In a recent paper, Bousquet-Mélou et al. [1] found, using the so called ascent sequences, the generating function for the number of -free posets of size n: . We extend this result in two ways. First, we find the generating function for -free posets when four statistics are taken into account, one of which is the number of minimal elements in a poset. Second, we show that if pn,k equals the number of -free posets of size n with k minimal elements, then . The second result cannot be derived from the first one by a substitution. Our enumeration results are extended to certain restricted permutations and to regular linearized chord diagrams through bijections in [1] and [2]. Finally, we define a subset of ascent sequences counted by the Catalan numbers and we discuss its relations with - and -free posets.