Bijective proofs for Eulerian numbers of types B and D

Autor: Luigi Santocanale

Publikováno v: Discrete Mathematics & Theoretical Computer Science, Vol vol. 23 no. 2, special issue..., Iss Special issues (2023)

Let $\Bigl\langle\matrix{n\cr k}\Bigr\rangle$, $\Bigl\langle\matrix{B_n\cr k}\Bigr\rangle$, and $\Bigl\langle\matrix{D_n\cr k}\Bigr\rangle$ be the Eulerian numbers in the types A, B, and D, respectively -- that is, the number of permutations of n ele

Externí odkaz: https://doaj.org/article/e9ecf42d58514d34a3d6f789afa8fe92

Unitless Frobenius quantales

Autor: Cédric de Lacroix, Luigi Santocanale

It is often stated that Frobenius quantales are necessarily unital. By taking negation as a primitive operation, we can define Frobenius quantales that may not have a unit. We develop the elementary theory of these structures and show, in particular,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1267d3254bad8ba5c12583589a724688
https://hal.science/hal-03661651v2/document

Skew metrics valued in Sugihara semigroups

Autor: Luigi Santocanale

Publikováno v: Lecture Notes in Computer Science
Relational and Algebraic Methods in Computer Science
Relational and Algebraic Methods in Computer Science, Feb 2021, Marseille, France. pp.396--412
Relational and Algebraic Methods in Computer Science-19th International Conference, RAMiCS 2021, Marseille, France, November 2-5, 2021, Proceedings, volume 13027 of Lecture Notes in Computer Science, pages 396--412. Springer, 2021.
RAMiCS 2021
RAMiCS 2021, Nov 2021, Marseille, France. pp.396-412, ⟨10.1007/978-3-030-88701-8_24⟩
Relational and Algebraic Methods in Computer Science ISBN: 9783030887001
RAMiCS

International audience; We consider skew metrics (equivalently, transitive relations that are tournaments, linear orderings) valued in Sugihara semigroups on autodual chains. We prove that, for odd chains and chains without a unit, skew metrics class

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0f9e69a24e48a6756f68a8a28622fcd4
https://hal.archives-ouvertes.fr/hal-03518407

Dualizing sup-preserving endomaps of a complete lattice

Autor: Luigi Santocanale

Publikováno v: Electronic Proceedings in Theoretical Computer Science
Applied Category Theory Conference 2020
Applied Category Theory Conference 2020, Jul 2020, Cambridge, United States
Proceedings 3rd Annual International Applied Category Theory Conference 2020 (ACT 2020), volume 333 of Electronic Proceedings in Theoretical Computer Science
ACT 2020
ACT 2020, Jul 2020, Cambridge, United States. pp.335-346, ⟨10.4204/EPTCS.333.23⟩

It is argued in (Eklund et al., 2018) that the quantale [L,L] of sup-preserving endomaps of a complete lattice L is a Girard quantale exactly when L is completely distributive. We have argued in (Santocanale, 2020) that this Girard quantale structure

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a00afbd2577b9f87ac54946c13ceaa81
https://hal.archives-ouvertes.fr/hal-02901445

The Involutive Quantaloid of Completely Distributive Lattices

Autor: Luigi Santocanale

Publikováno v: RAMICS 2020
RAMICS 2020, Uli Fahrenberg; Peter Jipsen; Michael Winter, Apr 2020, Palaiseau, France. pp.286-301
Relational and Algebraic Methods in Computer Science
Relational and Algebraic Methods in Computer Science ISBN: 9783030435196
RAMiCS

Let L be a complete lattice and let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \b

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0ee4af545b5d26237ad6f95f0bc2b0e1
https://hal.archives-ouvertes.fr/hal-02342655v2/document